Marcelo Fernandes Furtado Associated
Professor



Research
area

Variational and topological methods

Publications

Accepted 

On
a HardySobolev type inequality and applications (with J.L.
Carvalho and E.S. Medeiros) to appear in Comm. Contemp. Math. 

A
minimax theorem for locally Lipschitz functionals and
applications (with J.P.P.
Silva) to appear in Journal d'Analyse Mathématique 



77.  A Signchanging
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 

76.  Elliptic
equations with critical and supercritical growth at
the boundary (with R.F. Oliveira) J. Math. Anal. Appl. 536 (2024), pp. 128177 

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. 345359 

74.  Remarks
on a Sobolev embedding (with E.A.M. Abreu and E.S. Medeiros) Appl. Math. Lett. 147 (2024), Article 108846 



73.  On a critical SchrödingerPoisson
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. 159180 

72. 
Positive
and nodal ground state solutions for a critical Sch
dingerPoisson system with indefinite potentials (with Y. Wang
and Z. Zhang) J. Math. Anal. Appl. 526 (2023), pp. 127252 

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. 428446 

2022 

70. 
Indefinite
planar problem with exponential critical growth
(with K.C.V. Sousa) J. Convex Analysis 29 (2022), pp. 361370 

69. 
A sharp
HardySobolev inequality with boundary terms and
applications (with J.L. Carvalho and E.S. Medeiros) NoDEA Nonlinear Differential Equations Applications 29 (2022), article number 5 

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 

2021 

67. 


66. 
KirchhoffSchr dinger equation in R^2
with critical exponential growth and indefinite
potential (with H.R. Zanata) Comm. Contemp. Math. 23 (2021), pp. 2050030 

65. 
Fractional
elliptic systems with noncoecive potentials (with J.C.
Albuquerque and E.D. Silva) Z. Angew. Math. Phys. 72 (2021), Article 187 

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. 295308 

63. 
On
a zeromass (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 

62. 
Positive solution for an indefinite
fourthorder nonlocal problem (with J.P.P. Silva) Israel J. Math. 241 (2021), pp. 775794 

61. 
Critical
boundary value problems in the upper halfspace
(with J.P.P. Silva) Nonlinear Anal. 212 (2021), pp. 112441 

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. 877899 

59. 
Multiplicity of solutions for a
nonlinear boundary value problem in the upper
halfspace (with K.C.V. Sousa) J. Math. Anal. Appl. 493 (2021), pp. 124544 



58. 
Semilinear elliptic problems involving
exponential critical growth in the halfspace (with D.D.
Felix and E.S. Medeiros) Comm. Pure Appl. Anal. 19 (2020), pp. 49374953 

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 

56. 
Soliton
solutions for a generalized quasilinear elliptic
problem (with E.D. Silva and M.L. Silva) Potential Anal. 53 (2020), pp. 1097112 

55. 
Existence
and multiplicity of positive solutions for a
fourthorder elliptic equation (with G.M. Figueiredo
and J.P.P. Silva) Proc. Roy. Soc. Edinburgh Sect. A 150 (2020), pp. 10531069 



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. 793805 

53. 
Two
solutions for a planar equation with combined
nonlinearities and critical growth Proc. Amer. Math. Soc. 147 (2019), pp. 43974408 

52. 
Existence
of solution for an asymptotically linear
SchrodingerKirchhoff equation (with A.M. Batista) Potential Anal. 50 (2019), pp. 609619 

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. 199215 

50. 
An
elliptic equation with random potential and
supercritical nonlinearity (with L.C. Ferreira and L. Cioletti) Rev. Integr. Temas Mat. 37 (2019), pp. 116 

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 

48. 
Multiple
solutions for a critical Kirchhoff system (with L.D. Oliveira and J.P.P. Silva) Appl. Math. Lett. 91 (2019), pp. 97105 

2018 

47. 
Positive
and nodal solutions for a nonlinear Schr
dingerPoisson system with signchanging potentials (with A.M.
Batista) Nonlinear Anal. Real World Appl. 39 (2018), pp. 142156 

46. 
Solutions
for a Schr dingerKirchhoff Equation with Indefinite
Potentials (with A.M. Batista) Milan J. Math. 86 (2018), pp. 114 

2017 

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. 107126 

44. 
A
note on asymptotically periodic Schr dinger equations (with R. Marchi) Electron. J. Differential Equations 15 (2017), pp. 115 

43. 
Semilinear elliptic problems
with combined nonlinearities on the boundary (with R. Ruviaro and E.D. Silva) Ann. Mat. Pura Appl. 196 (2017), pp. 18871901, 2017 

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 

41. 
Multiple
solutions for a Kirchhoff equation with nonlinearity
having arbitrary growth (with H.R. Zanata) Bull. Aust. Math. Soc. 96 (2017), pp. 9810 

2016 

40. 
Positive
and nodal solutions for an elliptic equation with
critical growth (with B.N. Souza) Comm. Contemp. Math. 18 (2016), pp. 1550021 

39. 
Asymptotically
periodic superquadratic
Hamiltonian systems (with R. Marchi) J. Math. Anal. Appl. 433 (2016), pp. 712731 

38. 
Elliptic
equations with weight and combined nonlinearities (with J.P.P. Silva and B.N. Souza) Adv. Nonlinear Stud. 16 (2016), pp. 509517 

2015 

37. 
Superlinear elliptic problems
under the nonquadraticity
condition at infinity (with E.D. Silva) Proc. Roy. Soc. Edinburgh Sect. A 145 (2015), pp. 779790 

36. 
Nonquadraticity condition on superlinear problems (with E.D.
Silva) Progr. Nonlinear Differential Equations Appl. 86 (2015), pp. 245255 

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. 277291 

34. 
Existence
and multiplicity of selfsimilar solutions for heat
equations with nonlinear boundary conditions (with L.C. Ferreira and E.S. Medeiros) Calc. Var. Partial Differential Equations 54 (2015), p. 40654078 

2014 

33. 
A
note on the existence of positive solution for a
nonautonomous Schr dinger Poisson system (with L.A.
Maia and E.S. Medeiros) Progr. Nonlinear Differential Equations Appl. 85 (2014), pp. 277286 

32. 
An
obstacle problem in a plane domain with two solutions (with G.M. Figueiredo and M. Montenegro) Adv. Nonlinear Stud. 14 (2014), pp. 327338 

31. 
Quasilinear
Schr dinger equations with asymptotically linear
nonlinearities (with E.D. Silva and M.L. Silva) Ad. Nonlinear Stud. 14 (2014), pp. 671686 

30. 
Two
solutions for an elliptic equation with fast
increasing weight and concaveconvex nonlinearities (with R. Ruviaro and
J.P.P. Silva) J. Math. Anal. Appl. 416 (2014), pp. 698709 

29. 
A
TrudingerMoser inequality
in a weighted Sobolev
space and applications (with E.S. Medeiros and U.B.Severo) Math. Nach. 287 (2104), pp. 12551473 

2013 

28. 
Multiplicity
of selfsimilar solutions for a critical equation (with J.P.P.
Silva and M.S. Xavier) J. Differential Equations 254 (2013), pp. 27322743 

2012 

27. 
Positive
solutions for a quasilinear Schr dinger equation with
critical growth (with G.M. Figueiredo) J. Dynam. Differential Equations 24 (2012), pp. 1328 

2011 

26. 
Multiple
solutions for a semilinear
problem with combined terms and nonlinear boundary
condition (with R.Ruviaro) Nonlinear Anal. 74 (2011), no. 14, pp. 48204830 

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. 770785 

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. 25342548 

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. 15651586 

2010 

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. 23772396 

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. 10351055 

20. 
Multiple
solutions for resonant elliptic systems via reduction
method (with F.O.V. dePaiva) Bull. Aust. Math. Soc. 82 (2010), pp. 211220 

19. 
Multiple solutions for critical
elliptic systems via penalization method (with C.O.
Alves and G.M. Figueiredo) Differential Integral Equations 23 (2010), pp. 703723 

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. 181199 

2009 

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. 17451758 

2008 

16. 
Multiple
positive solutions for a quasilinear system of Schr
dinger equations (with
G.M. Figueiredo) NoDEA Nonlinear Differential Equations Applications 15 (2008), pp. 309333 

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. 353373 

2007 

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. 11791195 

13. 
Nodal solutions for a nonhomogeneous
elliptic equation with symmetry Topol. Meth. Nonlinear Anal. 29 (2007), pp. 6978 

12. 
Positive
solutions for some quasilinear equations with critical
and supercritical growth (with G.M. Figueiredo) Nonlinear Anal. 66 (2007), pp. 16001616 

2006 

11. 
A note on the number of nodal solutions
of an elliptic equation with symmetry Appl. Math. Lett. 19 (2006), no. 4, pp. 326331 

10. 
On the
number of positive solution of a quasilinear elliptic
problem (with
G.M. Figueiredo) Indiana Univ. Math. J. 55 (2006), pp. 18351856 

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. 705721 

08. 
Multiplicity
of solutions for resonant elliptic systems (with F.O.V. dePaiva) J. Math Anal. Appl. 319 (2006), pp. 435449 

2005 

07. 
Multiplicity of nodal solutions for a
critical quasilinear equation with symmetry Nonlinear Anal. 63 (2005), pp. 11531166 

06. 
A relation between the domain topology
and the number of minimal nodal solutions for a
quasilinear elliptic problem Nonlinear Anal. 62 (2005), pp. 615628 

05. 
Multiple minimal nodal solutions for a
quasilinear Schr dinger equation with symmetric
potential J. Math Anal. Appl. 304 (2005), pp. 170188 

2003 

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., 295304 

2002 

03. 
On a double resonant problem in Rn (with L.A. Maia and E.A.B. Silva) Differential Integral Equations 15 (2002), pp. 13351344 

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. 15151536 

2001 

01. 
Double
resonant problems which are locally nonquadratic
at infinity (with E.A.B. Silva) Electron. J. Diff. Eqns. Conf. 06 (2001), pp.155171 
Notas de aula de cursos de pósgraduação 
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 

Education 