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November  2009, 8(6): 2013-2035. doi: 10.3934/cpaa.2009.8.2013

Elliptic systems involving critical growth in dimension two

Paulo Rabelo 1,

1. 

Departamento de Matemática, Universidade Federal de Sergipe, 49100-000, São Cristóvão–SE, Brazil

Received  October 2008 Revised  March 2009 Published  August 2009

Using minimax methods we study the existence and multiplicity of solutions for a class of semilinear elliptic nonhomogeneous systems where the potentials can change sign and the nonlinearities may be unbounded in $x$ and behave like $\exp(\alpha s^2)$ when $|s|\rightarrow+\infty$. We establish the existence of two distinct solutions when the perturbations are suitably small.
Keywords: variational methods, Elliptic systems, Schrödinger equation, critical growth, Trudinger-Moser inequality..
Mathematics Subject Classification: Primary: 35J50, 35J55; Secondary: 35Q5.
Citation: Paulo Rabelo. Elliptic systems involving critical growth in dimension two. Communications on Pure and Applied Analysis, 2009, 8 (6) : 2013-2035. doi: 10.3934/cpaa.2009.8.2013
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