علی تقوی

In this paper, we consider the system 8>>< >>: 􀀀Δp(x)u = a(x)jujr1(x)−2u 􀀀 b(x)juj (x)−2u x 2 Ω 􀀀Δq(x)v = c(x)jvjr2(x)−2v 􀀀 d(x)jvj (x)−2v x 2 Ω u = v = 0 x 2 @Ω where Ω is a bounded domain in RN with smooth boundary, ;  > 0, p, q, r1, r2, and are continuous functions on ¯Ω satisfying appropriate conditions. We prove that for any  > 0, there exists ∗ sufficiently small, and  ∗ large enough such that for any  2 (0; ∗) [ ( ∗ ;1), the above system has a nontrivial weak solution. The proof relies on some variational arguments based on the Ekeland’s variational principle and some adequate variational methods.