RESEARCH


Research Interests

Existence, uniqueness and qualitative properties of solutions for nonlinear problems arising in mathematical physics, biology or differential geometry. Of particular interest are the problems presenting a lack of compactness, for which new tools in topology or Morse theory are required in order to detect solutions. I am also very interested in isoperimetric inequalities and their applications to derive uniqueness for nonlinear problems.



Publications

  1. Multi-bump bound states for a system of nonlinear Schrödinger equations, J. Differential Equations, to appear (with. Z.W. Tang).
  2. Minimal immersions of closed surfaces in hyperbolic three-manifolds, Geom. Dedicata, to appear (with Z. Huang).
  3. Uniqueness and symmetry of equilibria in a chemotaxis system, J. Reine Angew. Math. 654 (2011), 83-124 (with D. Horstmann).
  4. Exact multiplicity of nematic states for an Onsager model, Nonlinearity 23 (2010), 3157-3185 (with J. Vukadinovic).
  5. Numerical solution of the Helmholtz equation in an infinite strip by Wiener-Hopf factorization, Numer. Methods Partial Differential Equations 26 (2010), 1247-1274 (with F. Maggio and G. Rodriguez).
  6. Nonlocal elliptic boundary value problems related to chemotactic movement of mobile species, Proceedings of the RIMS Conference on "Mathematical Analysis on the Self-organization and Self-similarity", September 16-18, 2008, in Kyoto, RIMS Kokuroku Bessatsu B15, pp. 39-72, (2009) (with D. Horstmann).
  7. Eigenvalue problems with weights in Lorentz spaces, Calc. Var. Partial Differential Equations 36 (2009), 355-376 (with T.V. Anoop and M. Ramaswamy).
  8. A Minimax Theorem in the presence of unbounded Palais-Smale sequences, Israel J. Math. 172 (2009), 125-143 (with J. Hórak).
  9. Isoperimetric profile and uniqueness for Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 81-100.
  10. Gradient theory of phase transitions with a rapidly oscillating forcing term, Asym. Analysis 60 (2008), 29-59 (with N. Dirr and M. Novaga).
  11. Global bifurcation for semilinear elliptic problems, Recent Advances in Nonlinear Analysis, Edited by M. Chipot, C.S. Lin, D.H. Tsai, World Scientific, 2008, 197-216. (with M. Ramaswamy).
  12. Laplacian eigenvalues for mean zero functions with constant Dirichlet data, Forum Math. 20 (2008), 763-782 (with A. Greco).
  13. Best constant in some exponential Sobolev inequalities, Indiana Univ. Math. J. 57 (2008), 1907-1928 (with B. Kawohl).
  14. Existence of traveling wave solutions of invasion for Ginzburg-Landau-type problems in infinite cylinders, Arch. Ration. Mech. Anal. 188 (2008), 475-508 (with C. Muratov and M. Novaga).
  15. A deformation Lemma with an application to a mean field equation, Topol. Methods Nonlinear Anal. 30 (2007), 113-138.
  16. One-dimensional symmetry of periodic minimizers for a mean field equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 6 (2007), 269-290 (with C.S. Lin).
  17. Simplicity of the principal eigenvalue for indefinite quasilinear problems, Adv. Differential Equations 12 (2007), 407-434 (with B. Kawohl and S. Prashanth).
  18. Uniqueness of solutions for a mean field equation on torus, J. Differential Equations 229 (2006), 172-185 (with C.S. Lin).
  19. A blowing-up branch of solutions for a mean field equation, Calc. Var. Partial Differential Equations 26 (2006), 313-330.
  20. Gamma-convergence of the Allen-Cahn energy with a rapidly oscillating forcing term, Interfaces Free Bound 8 (2006), 47-78 (with N. Dirr and M. Novaga).
  21. Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight, Arch. Math. (Basel) 86 (2006), 79-89 (with S. Prashanth).
  22. On the uniqueness and simplicity of the principal eigenvalue, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 16 (2005), 132-142.
  23. A mean field equation on a torus: one-dimensional symmetry of solutions, Comm. PDE 30 (2005), 1315-1330 (with X. Cabré and M. Sanchón).
  24. A priori estimates and uniqueness for some mean field equations, J. Differential Equations 217 (2005), 154-178 (with L. Zhang).
  25. A Mountain Pass Theorem without Palais-Smale condition, C. R. Acad. Sci. Paris Ser. I Math. 341 (2005), 287-291.
  26. A Deformation Lemma for a Moser-Trudinger type functional, Nonlinear Anal. 63 (2005), 282-299.
  27. Gamma-star-shapedness for semilinear elliptic equations, Comm. Pure Appl. Anal. 4 (2005), 93-99 (with A. Greco).
  28. Some elliptic semilinear indefinite problems on RN, Proc. Roy. Soc. Edinburgh 134 (2004), 333-361 (with J. Giacomoni and M. Ramaswamy).
  29. Linear vs. nonlinear selection for the propagation speed of solutions of scalar reaction-diffusion equations invading an unstable equilibrium, Comm. Pure Appl. Math. 57 (2004), 616-636 (with C. Muratov and M. Novaga).
  30. Strong comparison principle for solutions of quasilinear equations, Proc. AMS 132 (2004), 1005-1011 (with S. Prashanth).
  31. A Dirichlet problem with asymptotically linear and sign changing nonlinearity, Rev. Mat. Complut. 16 (2003), 465-481 (with P. Magrone and H.S. Zhou).
  32. SU(3) Chern-Simons vortex theory and Toda systems, J. Differential Equations 184 (2002), 443-474 (with M. Nolasco).
  33. A Neumann problem in exterior domain, Manuscripta Math. 106 (2001), 63-74 (with D. Cao and H.S. Zhou).
  34. An application of the Artin-Schreier Theorem, Comm. Algebra 29 (2001), 4421-4424 (with J. Boéchat).
  35. Branches of solutions to a semilinear elliptic equations with singular coefficients on RN, Rend. Mat. Appl. 19 (1999), 489-506.
  36. The branch of positive solutions to a semilinear elliptic equation on RN, Rend. Sem. Mat. Univ. Padova 101 (1999), 229-262 (with H. Jeanjean and C.A. Stuart).
  37. Branches of solutions to semilinear elliptic equations on RN, Math. Z. 230 (1999), 79-105 (with H. Jeanjean and C.A. Stuart).


Conferences organized

Special seminars organized at CIAMCS (Center for Interdisciplinary Applied Mathematics and Computational Sciences)