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On existence of weak solutions of Neumann problem for quasilinear elliptic equations involving p-Laplacian in an unbounded domain

Hoang Quoc Toan|Trinh Thi Minh Hang
대한수학회 (The Korean Mathematical Society)|2011.11|대한수학회보 (Bulletin of the KMS)|제48권 제6호|pp. 1169-1182

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참고문헌

키워드

p-LaplacianNeumann problemMountain pass theoremthe weakly continuously differentiable functional
주제분류수학

초록

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form -div(h(x)|∇ u|^(p-2)∇ u)+b(x)|u|^(p-2)u= f(x,u) , p≥2 in an unbounded domain Ω ⊂ R^N, N≥ 3, with sufficiently smooth bounded boundary ∂Ω, where h(x) ∈ [수식], [기호]=Ω∪∂Ω, h(x)≥ 1 for all x ∈Ω. The proof of main results rely essentially on the arguments of variational method.

Abstract

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form -div(h(x)|∇ u|^(p-2)∇ u)+b(x)|u|^(p-2)u= f(x,u) , p≥2 in an unbounded domain Ω ⊂ R^N, N≥ 3, with sufficiently smooth bounded boundary ∂Ω, where h(x) ∈ [수식], [기호]=Ω∪∂Ω, h(x)≥ 1 for all x ∈Ω. The proof of main results rely essentially on the arguments of variational method.

참고문헌 (16)

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