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Marcelo Fernandes Furtado Associated
Professor
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Research
area
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Variational and topological methods
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Publications
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Accepted |
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| On
a Hardy-Sobolev type inequality and applications (with J.L.
Carvalho and E.S. Medeiros) to appear in Comm. Contemp. Math. |
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| A
minimax theorem for locally Lipschitz functionals and
applications (with J.P.P.
Silva) to appear in Journal d'Analyse Mathématique |
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| 77. | A Sign-changing
solution for an elliptic equation with critical growth
at the boundary (with J.P.P. Silva and K.C.V. Sousa) NoDEA Nonlinear Differential Equations Applications 31 (2024), article number 100 |
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| 76. | Elliptic
equations with critical and supercritical growth at
the boundary (with R.F. Oliveira) J. Math. Anal. Appl. 536 (2024), pp. 128177 |
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| 75. | Embedding
theorems for weighted Sobolev spaces in a borderline
case and applications (with J.L. Carvalho and E.S. Medeiros) Ann. Mat. Pura Appl. 203 (2024), pp. 345-359 |
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| 74. | Remarks
on a Sobolev embedding (with E.A.M. Abreu and E.S. Medeiros) Appl. Math. Lett. 147 (2024), Article 108846 |
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| 73. | On a critical Schrödinger-Poisson
system in R^2 with potentials vanishing at infinity
(with F.S.B.
Albuquerque, J.L. Carvalho and E.S. Medeiros) Topological Meth. Nonlinear Anal. 62 (2023), pp. 159-180 |
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| 72. |
Positive
and nodal ground state solutions for a critical Sch
dinger-Poisson system with indefinite potentials (with Y. Wang
and Z. Zhang) J. Math. Anal. Appl. 526 (2023), pp. 127252 |
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| 71. |
Hardy
inequality for domains with a geometric boundary
condition and applications (with E.A.M. Abreu, J.L. Carvalho and E.S.
Medeiros) Bulletin of the London Math. Society 55 (2023), pp. 428-446 |
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2022 |
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| 70. |
Indefinite
planar problem with exponential critical growth
(with K.C.V. Sousa) J. Convex Analysis 29 (2022), pp. 361-370 |
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| 69. |
A sharp
Hardy-Sobolev inequality with boundary terms and
applications (with J.L. Carvalho and E.S. Medeiros) NoDEA Nonlinear Differential Equations Applications 29 (2022), article number 5 |
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| 68. |
Two solutions for a singular elliptic
equation with critical growth at infinity (with K.C.V.
Sousa) Nonlinear Anal. Real World Appl. 63 (2022), pp. 103419 |
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2021 |
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| 67. |
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| 66. |
Kirchhoff-Schr dinger equation in R^2
with critical exponential growth and indefinite
potential (with H.R. Zanata) Comm. Contemp. Math. 23 (2021), pp. 2050030 |
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| 65. |
Fractional
elliptic systems with noncoecive potentials (with J.C.
Albuquerque and E.D. Silva) Z. Angew. Math. Phys. 72 (2021), Article 187 |
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| 64. |
Existence
and multiplicity of solutions for a Kirchhoff system
with critical growth (with L.D. Oliveira and J.P.P. Silva) Annales Fennici Mathematici 46 (2021), pp. 295-308 |
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| 63. |
On
a zero-mass (N,q)-Laplacian equation in R^N with
exponential critical growth (with J.L. Carvalho,
G.M. Figueiredo and E.S. Medeiros) Nonlinear Anal. 213 (2021), pp. 112488 |
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| 62. |
Positive solution for an indefinite
fourth-order nonlocal problem (with J.P.P. Silva) Israel J. Math. 241 (2021), pp. 775-794 |
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| 61. |
Critical
boundary value problems in the upper half-space
(with J.P.P. Silva) Nonlinear Anal. 212 (2021), pp. 112441 |
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| 60. |
On
a weighted trace embedding and applications to critical
boundary problems (with L.C. Ferreira, E.S.
Medeiros and J.P.P. Silva) Math. Nachr. 294 (2021), pp. 877-899 |
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| 59. |
Multiplicity of solutions for a
nonlinear boundary value problem in the upper
half-space (with K.C.V. Sousa) J. Math. Anal. Appl. 493 (2021), pp. 124544 |
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| 58. |
Semilinear elliptic problems involving
exponential critical growth in the half-space (with D.D.
Felix and E.S. Medeiros) Comm. Pure Appl. Anal. 19 (2020), pp. 4937-4953 |
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| 57. |
Kircchoff elliptic problems with
asymptotically linear or superlinear nonlinearities (with U.B.
Severo and E.D. Silva) Z. Angew. Math. Phys 71 (2020), Article 186 |
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| 56. |
Soliton
solutions for a generalized quasilinear elliptic
problem (with E.D. Silva and M.L. Silva) Potential Anal. 53 (2020), pp. 1097-112 |
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| 55. |
Existence
and multiplicity of positive solutions for a
fourth-order elliptic equation (with G.M. Figueiredo
and J.P.P. Silva) Proc. Roy. Soc. Edinburgh Sect. A 150 (2020), pp. 1053-1069 |
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| 54. |
Nodal
solution for a planar problem with fast increasing
weights (with G.M. Figueiredo
and R. Ruviaro) Topological Meth. Nonlinear Anal. 54 (2019), pp. 793-805 |
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| 53. |
Two
solutions for a planar equation with combined
nonlinearities and critical growth Proc. Amer. Math. Soc. 147 (2019), pp. 4397-4408 |
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| 52. |
Existence
of solution for an asymptotically linear
Schrodinger-Kirchhoff equation (with A.M. Batista) Potential Anal. 50 (2019), pp. 609-619 |
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| 51. |
Two
solutions for a fourth order nonlocal problem with
indefinite potentials (with G.M. Figueiredo
and J.P.P. Silva) Manuscripta Math. 160 (2019), pp. 199-215 |
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| 50. |
An
elliptic equation with random potential and
supercritical nonlinearity (with L.C. Ferreira and L. Cioletti) Rev. Integr. Temas Mat. 37 (2019), pp. 1-16 |
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| 49. |
Multiple
solutions for a Kirchhoff equation with critical
growth (with L.D. Oliveira and J.P.P. Silva) Z. Angew. Math. Phys. 70 (2019), Article 11 |
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| 48. |
Multiple
solutions for a critical Kirchhoff system (with L.D. Oliveira and J.P.P. Silva) Appl. Math. Lett. 91 (2019), pp. 97-105 |
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2018 |
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| 47. |
Positive
and nodal solutions for a nonlinear Schr
dinger-Poisson system with sign-changing potentials (with A.M.
Batista) Nonlinear Anal. Real World Appl. 39 (2018), pp. 142-156 |
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| 46. |
Solutions
for a Schr dinger-Kirchhoff Equation with Indefinite
Potentials (with A.M. Batista) Milan J. Math. 86 (2018), pp. 1-14 |
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2017 |
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| 45. |
On
a Class of Semilinear
Elliptic Eigenvalue Problems in R^2 (with E.S.
Medeiros and U.B.Severo) Proc. Edinb. Math. Soc. 60 (2017), pp. 107-126 |
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| 44. |
A
note on asymptotically periodic Schr dinger equations (with R. Marchi) Electron. J. Differential Equations 15 (2017), pp. 1-15 |
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| 43. |
Semilinear elliptic problems
with combined nonlinearities on the boundary (with R. Ruviaro and E.D. Silva) Ann. Mat. Pura Appl. 196 (2017), pp. 1887-1901, 2017 |
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| 42. |
Existence
of solution for a generalized quasilinear elliptic
problem (with E.D. Silva and M.L. Silva) J. Math. Phys. 58 (2017), pp. 031503 |
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| 41. |
Multiple
solutions for a Kirchhoff equation with nonlinearity
having arbitrary growth (with H.R. Zanata) Bull. Aust. Math. Soc. 96 (2017), pp. 98-10 |
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2016 |
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| 40. |
Positive
and nodal solutions for an elliptic equation with
critical growth (with B.N. Souza) Comm. Contemp. Math. 18 (2016), pp. 1550021 |
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| 39. |
Asymptotically
periodic superquadratic
Hamiltonian systems (with R. Marchi) J. Math. Anal. Appl. 433 (2016), pp. 712-731 |
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| 38. |
Elliptic
equations with weight and combined nonlinearities (with J.P.P. Silva and B.N. Souza) Adv. Nonlinear Stud. 16 (2016), pp. 509-517 |
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2015 |
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| 37. |
Superlinear elliptic problems
under the non-quadraticity
condition at infinity (with E.D. Silva) Proc. Roy. Soc. Edinburgh Sect. A 145 (2015), pp. 779-790 |
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| 36. |
Nonquadraticity condition on superlinear problems (with E.D.
Silva) Progr. Nonlinear Differential Equations Appl. 86 (2015), pp. 245-255 |
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| 35. |
Quasilinear
elliptic problems under asymptotically linear
conditions at infinity and at the origin (with E.D.
Silva and M.L. Silva) Z. Angew. Math. Phys. 66 (2015), pp. 277-291 |
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| 34. |
Existence
and multiplicity of self-similar solutions for heat
equations with nonlinear boundary conditions (with L.C. Ferreira and E.S. Medeiros) Calc. Var. Partial Differential Equations 54 (2015), p. 4065-4078 |
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2014 |
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| 33. |
A
note on the existence of positive solution for a
non-autonomous Schr dinger- Poisson system (with L.A.
Maia and E.S. Medeiros) Progr. Nonlinear Differential Equations Appl. 85 (2014), pp. 277-286 |
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| 32. |
An
obstacle problem in a plane domain with two solutions (with G.M. Figueiredo and M. Montenegro) Adv. Nonlinear Stud. 14 (2014), pp. 327-338 |
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| 31. |
Quasilinear
Schr dinger equations with asymptotically linear
nonlinearities (with E.D. Silva and M.L. Silva) Ad. Nonlinear Stud. 14 (2014), pp. 671-686 |
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| 30. |
Two
solutions for an elliptic equation with fast
increasing weight and concave-convex nonlinearities (with R. Ruviaro and
J.P.P. Silva) J. Math. Anal. Appl. 416 (2014), pp. 698-709 |
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| 29. |
A
Trudinger-Moser inequality
in a weighted Sobolev
space and applications (with E.S. Medeiros and U.B.Severo) Math. Nach. 287 (2104), pp. 1255-1473 |
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2013 |
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| 28. |
Multiplicity
of self-similar solutions for a critical equation (with J.P.P.
Silva and M.S. Xavier) J. Differential Equations 254 (2013), pp. 2732-2743 |
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2012 |
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| 27. |
Positive
solutions for a quasilinear Schr dinger equation with
critical growth (with G.M. Figueiredo) J. Dynam. Differential Equations 24 (2012), pp. 13-28 |
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2011 |
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| 26. |
Multiple
solutions for a semilinear
problem with combined terms and nonlinear boundary
condition (with R.Ruviaro) Nonlinear Anal. 74 (2011), no. 14, pp. 4820-4830 |
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| 25. |
Multiplicity
of solutions for homogeneous elliptic systems with
critical growth (with J.P.P. Silva) J. Math Anal. Appl. 385 (2011), no. 2, pp. 770-785 |
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| 24. |
On
the number of solutions of NLS equations with
magnetics fields in expanding domains (with C.O.
Alves and G.M. Figueiredo) J. Differential Equations 251 (2011), pp. 2534-2548 |
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| 23. |
Multiple
solutions for a Schr dinger equation with magnetic
fields (with C.O. Alves and G.M. Figueiredo) Comm. in Partial Differential Equations 36 (2011), no. 9, pp. 1565-1586 |
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2010 |
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| 22. |
Multiplicity
and concentration of solutions for elliptic systems
with vanishing potentials (with E.A.B. Silva and M.S. Xavier) J. Differential Equations 249 (2010), pp. 2377-2396 |
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| 21. |
On
a class of nonlinear elliptic equations with fast
increasing weight and critical growth (with O.H. Myiagaki and J.P.P. Silva) J. Differential Equations 249 (2010), pp. 1035-1055 |
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| 20. |
Multiple
solutions for resonant elliptic systems via reduction
method (with F.O.V. dePaiva) Bull. Aust. Math. Soc. 82 (2010), pp. 211-220 |
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| 19. |
Multiple solutions for critical
elliptic systems via penalization method (with C.O.
Alves and G.M. Figueiredo) Differential Integral Equations 23 (2010), pp. 703-723 |
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| 18. |
Multiple solutions for a null mass
Neumann problem in exterior domains (with L.A.
Maia and E.S. Medeiros) Adv. Differential Equations 15 (2010), pp. 181-199 |
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2009 |
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| 17. |
Multiplicity
of solutions for elliptic systems via local mountain
pass method (with C.O. Alves and G.M. Figueiredo) Comm. Pure. Appl. Anal. 8 (2009), pp. 1745-1758 |
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2008 |
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| 16. |
Multiple
positive solutions for a quasilinear system of Schr
dinger equations (with
G.M. Figueiredo) NoDEA Nonlinear Differential Equations Applications 15 (2008), pp. 309-333 |
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| 15. |
Positive
and nodal solutions for a nonlinear Schr dinger
equation with indefinite potential (with
L.A. Maia and E.S. Medeiros) Adv. Nonlinear Studies 8 (2008), pp. 353-373 |
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2007 |
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| 14. |
Positive solutions for nonlinear
elliptic equations with fast increasing weights (with
F. Catrina and M. Montenegro) Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), pp. 1179-1195 |
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| 13. |
Nodal solutions for a nonhomogeneous
elliptic equation with symmetry Topol. Meth. Nonlinear Anal. 29 (2007), pp. 69-78 |
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| 12. |
Positive
solutions for some quasilinear equations with critical
and supercritical growth (with G.M. Figueiredo) Nonlinear Anal. 66 (2007), pp. 1600-1616 |
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2006 |
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| 11. |
A note on the number of nodal solutions
of an elliptic equation with symmetry Appl. Math. Lett. 19 (2006), no. 4, pp. 326-331 |
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| 10. |
On the
number of positive solution of a quasilinear elliptic
problem (with
G.M. Figueiredo) Indiana Univ. Math. J. 55 (2006), pp. 1835-1856 |
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| 09. |
Multiplicity
of positive solutions for a class of elliptic equation
in divergence form (with G.M. Figueiredo) J. Math. Anal. Appl. 321 (2006), pp. 705-721 |
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| 08. |
Multiplicity
of solutions for resonant elliptic systems (with F.O.V. dePaiva) J. Math Anal. Appl. 319 (2006), pp. 435-449 |
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2005 |
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| 07. |
Multiplicity of nodal solutions for a
critical quasilinear equation with symmetry Nonlinear Anal. 63 (2005), pp. 1153-1166 |
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| 06. |
A relation between the domain topology
and the number of minimal nodal solutions for a
quasilinear elliptic problem Nonlinear Anal. 62 (2005), pp. 615-628 |
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| 05. |
Multiple minimal nodal solutions for a
quasilinear Schr dinger equation with symmetric
potential J. Math Anal. Appl. 304 (2005), pp. 170-188 |
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2003 |
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| 04. |
Systems
with coupling in Rn for a class of noncoercive
potentials (with L.A.Maia
and E.A.B. Silva) Dynamical systems and differential equations (Wilmington, NC, 2002). Discrete Contin. Dyn. Syst. (2003), suppl., 295-304 |
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2002 |
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| 03. |
On a double resonant problem in Rn (with L.A. Maia and E.A.B. Silva) Differential Integral Equations 15 (2002), pp. 1335-1344 |
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| 02. |
Solutions
for a resonant elliptic system with coupling in Rn (with L.A.Maia
and E.A.B. Silva) Comm. in Partial Differential Equations 27 (2002), pp. 1515-1536 |
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2001 |
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| 01. |
Double
resonant problems which are locally nonquadratic
at infinity (with E.A.B. Silva) Electron. J. Diff. Eqns. Conf. 06 (2001), pp.155-171 |
Monographs (in portuguese)
| Notas de aula de cursos de pós-graduação |
| Notas
de aula do curso de EDP2 (vers o 2.0, Maio/2023) |
| Notas de aula do curso de M todos
Variacionais (ves o
1.1) |
Trabalhos em nível de graduação |
| O grau
topológico de Brower
(with other
authors) Trab. Graduação em Mat. 002/97, UnB |
| O teorema
de Jordan (with
other authors) Trab. Graduação em Mat. 001/97, UnB |
| Métodos
variacionais - uma introdução Trab. Graduação em Mat. 002/96, UnB |
| Algumas realizações
de Charles Hermite Trab. Graduação em Mat. 001/96, UnB |
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Education |
Thesis: Multiplicidade de soluções nodais para problemas elípticos quasilineares.
Advisor: Prof. Djairo Guedes de Figueiredo.
Master Degree, Mathematics, Depto. Matem tica, UnB, 1999.
Thesis: Um teorema do tipo Ponto de Sela com aplicação a um problema elíptico semilinear com dupla ressonância.
Advisor: Prof. Elves A.B. Silva.