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 for nonlinear partial differential equations.


 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.


 Publications

Papers

  1. Existence of solution for an asymptotically linear Schrodinger-Kirchhoff equation (with A.M. Batista)
    to appear in Potential Analysis

  2. Existence and multiplicity of positive solutions for a fourth-order elliptic equation (with G.M. Figueiredo and J.P.P. Silva)
    to appear in Proc. Royal Soc. Edinburgh, Section A

  3. Two solutions for a fourth order nonlocal problem with indefinite potentials (with G.M. Figueiredo and J.P.P. Silva)
    to appear in Manuscripta Mathematica

  4. An elliptic equation with random potential and supercritical nonlinearity (with L.C. Ferreira and L. Cioletti)
    to appear in Integraciones

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

  6. Solutions for a Schrödinger-Kirchhoff Equation with Indefinite Potentials (with A.M. Batista)
    Milan Journal of Mathematics 86 (2018), pp. 1-14.

  7. On a Class of Semilinear Elliptic Eigenvalue Problems in R^2 (with E.S. Medeiros and U.B.Severo)
    Proceedings of the Edinburgh Mathematical Society 60 (2017), pp. 107-126.

  8. A note on asymptotically periodic Schrödinger equations (with R. Marchi)
    Electronic Journal of Differential Equations 15 (2017), pp. 1-15

  9. Semilinear elliptic problems with combined nonlinearities on the boundary (with R. Ruviaro and E.D. Silva)
    Annali di Matematica Pura Ed Applicata  196 (2017), pp. 1887-1901, 2017

10.  Existence of solution for a generalized quasilinear elliptic problem (with E.D. Silva and M.L. Silva)
Journal of Mathematical Physics 58 (2017), pp. 031503

  1. Multiple solutions for a Kirchhoff equation with nonlinearity having arbitrary growth (with H.R. Zanata)
    Bulletin of the Australian Mathematical Society 96 (2017), pp. 98-109

  2. Positive and nodal solutions for an elliptic equation with critical growth (with B.N. Souza)
    Communications in Contemporary Mathematics 18 (2016), pp. 1550021

  3. Asymptotically periodic superquadratic Hamiltonian systems (with R. Marchi)
    Journal of Mathematical Analysis and Applications 433 (2016), pp. 712-731

  4. Elliptic equations with weight and combined nonlinearities (with J.P.P. Silva and B.N. Souza)
    Advanced Nonlinear Studies 16 (2016), pp. 509-517

  5. Superlinear elliptic problems under the non-quadraticity condition at infinity (with E.D. Silva)
    Proc. Royal Soc. Edinburgh, Section A 145 (2015), pp. 779-790

  6. Nonquadraticity condition on superlinear problems (with E.D. Silva)
    Progress in Nonlinear Differential Equations and their Applications 86 (2015), pp. 245-255

  7. Quasilinear elliptic problems under asymptotically linear conditions at infinity and at the origin (with E.D. Silva and M.L. Silva)
    Zeitschrift fur Angewandte Mathematik und Physik 66 (2015), pp. 277-291

  8. Existence and multiplicity of self-similar solutions for heat equations with nonlinear boundary conditions (with L.C. Ferreira and E.S. Medeiros)
    Calculus of Variations and Partial Differential Equations 54 (2015), p. 4065-4078

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

  10. An obstacle problem in a plane domain with two solutions (with G.M. Figueiredo and M. Montenegro)
    Advanced Nonlinear Studies 14 (2014), pp. 327-338

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

  12. Two solutions for an elliptic equation with fast increasing weight and concave-convex nonlinearities (with R. Ruviaro and J.P.P. Silva)
    Journal of Mathematical Analysis and Applications 416 (2014), pp. 698-709

  13. A Trudinger-Moser inequality in a weighted Sobolev space and applications (with E.S. Medeiros and U.B.Severo)
    Mathematische Nachrichten 287 (2104), pp. 1255-1473

  14. Multiplicity of self-similar solutions for a critical equation (with J.P.P. Silva and M.S. Xavier)
    Journal of Differential Equations 254 (2013), pp. 2732-2743

  15. Positive solutions for a quasilinear Schrödinger equation with critical growth (with G.M. Figueiredo)
    J. Dyn. Diff. Equat. 24 (2012), pp. 13-28

  16. Multiple solutions for a semilinear problem with combined terms and nonlinear boundary condition (with R.Ruviaro)
    Nonlinear Analysis 74 (2011), no. 14, pp. 4820-4830

  17. 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

  18. On the number of solutions of NLS equations with magnetics fields in expanding domains (with C.O. Alves and G.M. Figueiredo)
    Journal of Differential Equations 251 (2011), pp. 2534-2548

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

  20. Multiplicity and concentration of solutions for elliptic systems with vanishing potentials (with E.A.B. Silva and M.S. Xavier)
    Journal of 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)
    Journal of Differential Equations 249 (2010), pp. 1035-1055

  22. Multiple solutions for resonant elliptic systems via reduction method (with F.O.V. dePaiva)
    Bulletin of the Australian Mathematical Society 82 (2010), pp. 211-220

  23. Multiple solutions for critical elliptic systems via penalization method (with C.O. Alves and G.M. Figueiredo)
    Differential and Integral Equations 23 (2010), pp. 703-723.

  24. Multiple solutions for a null mass Neumann problem in exterior domains (with L.A. Maia and E.S. Medeiros)
    Advances in Differential Equations 15 (2010), pp. 181-199

  25. Multiplicity of solutions for elliptic systems via local mountain pass method (with C.O. Alves and G.M. Figueiredo)
    Communications on Pure and Applied Analysis 8 (2009), pp. 1745-1758

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

  27. Positive and nodal solutions for a nonlinear Schrödinger equation with indefinite potential (with L.A. Maia and E.S. Medeiros)
    Advanced Nonlinear Studies 8 (2008), pp. 353-373
     
  28. Positive solutions for nonlinear elliptic equations with fast increasing weights (with F. Catrina and M. Montenegro)
    Proc. Royal Soc. Edinburgh, Section A 137 (2007), pp. 1179-1195
     
  29. Nodal solutions for a nonhomogeneous elliptic equation with symmetry
    Topol. Methods in Nonlinear Analysis 29 (2007), pp. 69-78
     
  30. Positive solutions for some quasilinear equations with critical and supercritical growth (with G.M. Figueiredo)
    Nonlinear Analysis 66 (2007), no. 7, pp. 1600-1616
     
  31. A note on the number of nodal solutions of an elliptic equation with symmetry
    Applied Math. Letters 19 (2006), no. 4, pp. 326-331
     
  32. On the number of positive solution of a quasilinear elliptic problem (with G.M. Figueiredo)
    Indiana Univ. Math. J. 55 (2006), no. 6, pp. 1835-1856
     
  33. Multiplicity of positive solutions for a class of elliptic equation in divergence form (with G.M. Figueiredo)
    J. Math. Anal. Appl. 321 (2006), no. 2, pp. 705-721
     
  34. Multiplicity of solutions for resonant elliptic systems (with F.O.V. dePaiva)
    J. Math Anal. Appl. 319 (2006), no. 2, pp. 435-449
     
  35. Multiplicity of nodal solutions for a critical quasilinear equation with symmetry
    Nonlinear Analysis 63 (2005), no.4, pp. 1153-1166
     
  36. A relation between the domain topology and the number of minimal nodal solutions for a quasilinear elliptic problem
    Nonlinear Analysis 62 (2005), no.4, pp. 615-628
     
  37. Multiple minimal nodal solutions for a quasilinear Schrödinger equation with symmetric potential
    J. Math Anal. Appl. 304 (2005), no.1, pp. 170-188
     
  38. 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
     
  39. On a double resonant problem in Rn (with L.A. Maia and E.A.B. Silva)
    Diff. Int. Equations 15 (2002), no.11, pp. 1335-1344
     
  40. Solutions for a resonant elliptic system with coupling in Rn  (with L.A.Maia and E.A.B. Silva)
    Comm. in PDE 27 (2002), no. 7&8, pp. 1515-1536

  41. 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)


 Last update in September, 2018.