Existence of Solutions for a Variable Exponent System without PS ConditionsElectronic Journal of Differential Equations
AbstractIn 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 N , − div |∇v| q(x)−2∇v) + |v| q(x)−2 v = λb(x)|v| δ(x)−2 v + Fv(x, u, v) in R N , u ∈ W1,p(·) (R N ), v ∈ W1,q(·) (R N ), 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.
Citation InformationLi Yin, Yuan Liang, Qihu Zhang and Chunshan Zhao. "Existence of Solutions for a Variable Exponent System without PS Conditions" Electronic Journal of Differential Equations Vol. 2015 Iss. 63 (2015) p. 1 - 23
Available at: http://works.bepress.com/chunshan_zhao/21/