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On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

Candela, Anna MariaSquassina, Marco — 2003

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30 By means of a suitable nonsmooth critical point theory for lower semicontinuous functionals we prove the existence of infinitely many solutions for a class of quasilinear Dirichlet problems with symmetric non-linearities having a one-sided growth condition of exponential type. The research of the authors was partially supported by the MIUR project “Variational and topological methods in the study of nonlinear...

Semiclassical states for weakly coupled nonlinear Schrödinger systems

Eugenio MontefuscoBenedetta PellacciMarco Squassina — 2008

Journal of the European Mathematical Society

We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.

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