Abstract
Abstract In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δ p(x) u = λ k(x) uq ± h(x) ur under Robin boundary condition in a regular open bounded domain Ω of ℝ N , N ≥ 2. Δ p(x) is the p(x)-Laplacian operator where p ∈ C 1(Ω) and p > 1. Our proofs are based on the sub solution-super solution method and also on variational arguments.
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