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
Multi-bump bound states for a system of nonlinear Schrödinger equations,
J. Differential Equations, to appear (with. Z.W. Tang).
Minimal immersions of closed surfaces in hyperbolic three-manifolds,
Geom. Dedicata, to appear (with Z. Huang).
Uniqueness and symmetry of equilibria in a chemotaxis system,
J. Reine Angew. Math. 654 (2011), 83-124 (with D. Horstmann).
Exact multiplicity of nematic states for an Onsager model,
Nonlinearity 23 (2010), 3157-3185 (with J. Vukadinovic).
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).
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).
Eigenvalue problems with weights in Lorentz spaces,
Calc. Var. Partial Differential Equations 36 (2009), 355-376 (with T.V.
Anoop and M. Ramaswamy).
A Minimax Theorem in the presence of unbounded Palais-Smale sequences,
Israel J. Math. 172 (2009), 125-143 (with J. Hórak).
Isoperimetric profile and uniqueness for Neumann problems,
Ann. Inst. H. Poincaré Anal. Non Linéaire,
26 (2009), 81-100.
Gradient theory of phase transitions with a rapidly oscillating forcing term,
Asym. Analysis 60 (2008), 29-59 (with N. Dirr and M. Novaga).
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).
Laplacian eigenvalues for mean zero functions with constant Dirichlet data,
Forum Math. 20 (2008), 763-782 (with A. Greco).
Best constant in some exponential Sobolev inequalities,
Indiana Univ. Math. J. 57 (2008), 1907-1928 (with B. Kawohl).
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).
A deformation Lemma with an application to a mean field equation,
Topol. Methods Nonlinear Anal. 30 (2007), 113-138.
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).
Simplicity of the principal eigenvalue for indefinite quasilinear problems,
Adv. Differential Equations 12 (2007), 407-434
(with B. Kawohl and S. Prashanth).
Uniqueness of solutions for a mean field equation on torus,
J. Differential Equations 229 (2006), 172-185 (with C.S. Lin).
A blowing-up branch of solutions for a mean field equation,
Calc. Var. Partial Differential Equations 26 (2006), 313-330.
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).
Simplicity of principal eigenvalue for p-Laplace operator with singular indefinite weight,
Arch. Math. (Basel) 86 (2006), 79-89 (with S. Prashanth).
On the uniqueness and simplicity of the principal eigenvalue,
Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 16 (2005), 132-142.
A mean field equation on a torus: one-dimensional symmetry of solutions,
Comm. PDE 30 (2005), 1315-1330
(with X. Cabré and M. Sanchón).
A priori estimates and uniqueness for some mean field equations,
J. Differential Equations 217 (2005), 154-178
(with L. Zhang).
A Mountain Pass Theorem without Palais-Smale condition,
C. R. Acad. Sci. Paris Ser. I Math. 341 (2005), 287-291.
A Deformation Lemma for a Moser-Trudinger type functional,
Nonlinear Anal. 63 (2005), 282-299.
Gamma-star-shapedness for semilinear elliptic equations,
Comm. Pure Appl. Anal. 4 (2005), 93-99
(with A. Greco).
Some elliptic semilinear indefinite problems on RN,
Proc. Roy. Soc. Edinburgh 134 (2004), 333-361
(with J. Giacomoni and M. Ramaswamy).
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).
Strong comparison principle for solutions of quasilinear equations,
Proc. AMS 132 (2004), 1005-1011
(with S. Prashanth).
A Dirichlet problem with asymptotically linear and sign changing nonlinearity,
Rev. Mat. Complut. 16 (2003), 465-481
(with P. Magrone and H.S. Zhou).
SU(3) Chern-Simons vortex theory and Toda systems,
J. Differential Equations 184 (2002), 443-474
(with M. Nolasco).
A Neumann problem in exterior domain,
Manuscripta Math. 106 (2001), 63-74
(with D. Cao and H.S. Zhou).
An application of the Artin-Schreier Theorem,
Comm. Algebra 29 (2001), 4421-4424
(with J. Boéchat).
Branches of solutions to a semilinear elliptic equations with singular
coefficients on RN,
Rend. Mat. Appl. 19 (1999), 489-506.
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).
Branches of solutions to semilinear elliptic equations on RN,
Math. Z. 230 (1999), 79-105
(with H. Jeanjean and C.A. Stuart).
Special seminars organized at
(Center for Interdisciplinary Applied Mathematics and Computational Sciences)