Existence of Solutions for a Variable Exponent System without Ps Conditions

In this article, we study the existence of solution for the following elliptic system of variable exponents with perturbation terms − div |∇u|p(x)−2∇u) + |u|p(x)−2u = λa(x)|u|γ(x)−2u+ Fu(x, u, v) in R , − div |∇v|q(x)−2∇v) + |v|q(x)−2v = λb(x)|v|δ(x)−2v + Fv(x, u, v) in R , u ∈W 1,p(·)(RN ), v ∈W 1,q(·)(RN ), where the corresponding functional does not satisfy PS conditions. We obtain a sufficient condition for the existence of solution and also present a result on asymptotic behavior of solutions at infinity.