Marcelo Fernandes Furtado

Associated Professor


 Universidade de BrasíliaDepartamento de Matemática
 70919-900, Brasília-DF, Brazil
 
 E-mail to: mfurtado@unb.br

 CNPq - CV
 


 Research area

Variational and topological methods


 Publications

 



Accepted


On a weighted trace embedding and applications to critical boundary problems (with L.C. Ferreira, E.S. Medeiros and J.P.P. Silva)
to appear in Mathematische Nachriten

Existence and multiplicity of solutions for a Kirchhoff system with critical growth (with L.D. Oliveira and J.P.P. Silva)
to appear in Annales Academiae Scientiarum Fennicae

Kirchhoff-Schrödinger equation in R^2 with critical exponential growth and indefinite potential (with H.R. Zanata)
to appear in
Comm. in Contemp. Math.

Positive solution for an indefinite fourth-order nonlocal problem (with J.P.P. Silva)
to appear in Israel J. Math.


2021

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


2020

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
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. 1097-112
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


2019

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
53.

Two solutions for a planar equation with combined nonlinearities and critical growth
Proc. Amer. Math. Soc. 147 (2019), pp. 4397-4408
52.

Existence of solution for an asymptotically linear Schrodinger-Kirchhoff equation (with A.M. Batista)
Potential Anal. 50 (2019), pp. 609-619
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
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
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. 97-105


2018

47.

Positive and nodal solutions for a nonlinear Schrödinger-Poisson system with sign-changing potentials (with A.M. Batista)
Nonlinear Anal. Real World Appl. 39 (2018), pp. 142-156
46.

Solutions for a Schrödinger-Kirchhoff Equation with Indefinite Potentials (with A.M. Batista)
Milan J. Math. 86 (2018), pp. 1-14


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. 107-126
44.

A note on asymptotically periodic Schrödinger equations (with R. Marchi)
Electron. J. Differential Equations 15 (2017), pp. 1-15
43.

Semilinear elliptic problems with combined nonlinearities on the boundary (with R. Ruviaro and E.D. Silva)
Ann. Mat. Pra Appl.   196 (2017), pp. 1887-1901, 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. 98-10


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. 712-731
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


2015

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
36.

Nonquadraticity condition on superlinear problems (with E.D. Silva)
Progr. Nonlinear Differential Equations Appl. 86 (2015), pp. 245-255
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
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


2014

33.

A note on the existence of positive solution for a non-autonomous Schrödinger- Poisson system (with L.A. Maia and E.S. Medeiros)
Progr. Nonlinear Differential Equations Appl. 85 (2014), pp. 277-286
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
31.

Quasilinear Schrödinger equations with asymptotically linear nonlinearities (with E.D. Silva and M.L. Silva)
Ad. Nonlinear Stud. 14 (2014), pp. 671-686
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
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


2013

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


2012

27.

Positive solutions for a quasilinear Schrödinger equation with critical growth (with G.M. Figueiredo)
J. Dynam. Differential Equations 24 (2012), pp. 13-28


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. 4820-4830
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
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
23.

Multiple solutions for a Schrödinger equation with magnetic fields (with C.O. Alves and G.M. Figueiredo)
Comm. in Partial Differential Equations 36 (2011), no. 9, pp. 1565-1586


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. 2377-2396
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
20.

Multiple solutions for resonant elliptic systems via reduction method (with F.O.V. dePaiva)
Bull. Aust. Math. Soc. 82 (2010), pp. 211-220
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
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


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. 1745-1758


2008

16.

Multiple positive solutions for a quasilinear system of Schrödinger equations (with G.M. Figueiredo)
NoDEA Nonlinear Differential Equations Applications 15 (2008), pp. 309-333
15.

Positive and nodal solutions for a nonlinear Schrödinger equation with indefinite potential (with L.A. Maia and E.S. Medeiros)
Adv. Nonlinear Studies 8 (2008), pp. 353-373


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. 1179-1195
13.

Nodal solutions for a nonhomogeneous elliptic equation with symmetry
Topol. Meth. Nonlinear Anal. 29 (2007), pp. 69-78
12.

Positive solutions for some quasilinear equations with critical and supercritical growth (with G.M. Figueiredo)
Nonlinear Anal. 66 (2007), pp. 1600-1616


2006

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
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
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
08.

Multiplicity of solutions for resonant elliptic systems (with F.O.V. dePaiva)
J. Math Anal. Appl. 319 (2006), pp. 435-449


2005

07.

Multiplicity of nodal solutions for a critical quasilinear equation with symmetry
Nonlinear Anal. 63 (2005), pp. 1153-1166
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
05.

Multiple minimal nodal solutions for a quasilinear Schrödinger equation with symmetric potential
J. Math Anal. Appl. 304 (2005), pp. 170-188


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., 295-304


2002

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
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


2001

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 (versão 1.2)
Notas de aula do curso de Métodos Variacionais (vesão 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
PhD, Mathematics, IMECC, UNICAMP, 2004.
Thesis: Multiplicidade de soluções nodais para problemas elípticos quasilineares.
Advisor: Prof. Djairo Guedes de Figueiredo.

Master Degree, Mathematics, Depto. Matemática, UnB, 1999.
ThesisUm teorema do tipo Ponto de Sela com aplicação a um problema elíptico semilinear com dupla ressonância.
Advisor: Prof. Elves A.B. Silva.


 Last update in September 2020