Abstract
We obtain the existence of a nontrivial solution for a class of subcritical elliptic systems with indefinite weights in . The proofs base on Trudinger-Moser inequality and a generalized linking theorem introduced by Kryszewski and Szulkin.
Highlights
In this paper, we study the existence of a nontrivial solution for the following systems of two semilinear coupled Poisson equations P−Δu u g x, v, x ∈ R2, −Δv v f x, u, x ∈ R2, 1.1 where f x, t and g x, t are continuous functions on R2 × R and have the maximal growth on t which allows to treat problem P variationally, Δ is the Laplace operator.Recently, there exists an extensive bibliography in the study of elliptic problem in RN 1–6
Received 31 October 2007; Accepted 4 March 2008 Recommended by Zhitao Zhang We obtain the existence of a nontrivial solution for a class of subcritical elliptic systems with indefinite weights in R2
We study the existence of a nontrivial solution for the following systems of two semilinear coupled Poisson equations
Summary
We study the existence of a nontrivial solution for the following systems of two semilinear coupled Poisson equations P−Δu u g x, v , x ∈ R2, −Δv v f x, u , x ∈ R2, 1.1 where f x, t and g x, t are continuous functions on R2 × R and have the maximal growth on t which allows to treat problem P variationally, Δ is the Laplace operator.Recently, there exists an extensive bibliography in the study of elliptic problem in RN 1–6. Received 31 October 2007; Accepted 4 March 2008 Recommended by Zhitao Zhang We obtain the existence of a nontrivial solution for a class of subcritical elliptic systems with indefinite weights in R2. We study the existence of a nontrivial solution for the following systems of two semilinear coupled Poisson equations They obtained the decay, symmetry, and existence of solutions for problem 1.2 .
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