- 期刊
MULTIPLE SOLUTIONS FOR A PROBLEM WITH RESONANCE INVOLVING THE p-LAPLACIAN
並列摘要
In this paper we will investigate the existence of multiple solutions for the problem (P) –Δ_pu + g(x, u) = λ_1h(x) |u|^(p−2) u, in Ω, u∈ H_0^(1,p)_0 (Ω) where Δ_pu = div _|∇u|^(p-2) ∇u_ is the p-Laplacian operator, Ω ⊆ IR^N is a bounded domain with smooth boundary, h and g are bounded functions, N ≥ 1 and 1 ＜ p ＜ ∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P).
並列關鍵字
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