Constant Sign Solutions for Variable Exponent System Neumann Boundary Value Problems with Singular Coefficient. (7th April 2014) - Wu, Xianbin
Abstract : We deal with the existence of constant sign solutions for the following variable exponent system Neumann boundary value problem: - div ( | ∇ u | p ( x ) - 2 ∇ u ) + λ | u | p ( x ) - 2 u = F u ( x, u, v )   in   Ω,   - div ( | ∇ v | q ( x ) - 2 ∇ v ) + λ | v | q ( x ) - 2 v = F v ( x, u, v ) in Ω,   ∂ u / ∂ γ = 0 = ∂ v / ∂ γ   on   ∂ Ω . We give several sufficient conditions for the existence of the constant sign solutions, when F ( x, ·, · ) satisfies neither sub-(p ( x ), q ( x ) ) growth condition, nor Ambrosetti-Rabinowitz condition (subcritical). In particular, we obtain the existence of eight constant sign solutions.