Weak solution of a Neumann boundary value problem with 𝑝(𝑥)-Laplacian-like operator

Mohamed El Ouaarabi, C. Allalou, S. Melliani
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引用次数: 6

Abstract

Abstract In this paper, we study the existence of a weak solution for a class of Neumann boundary value problems for equations involving the p ⁢ ( x ) p(x) -Laplacian-like operator. Using a topological degree theory for a class of demicontinuous operators of generalized ( S + ) (S_{+}) -type and the theory of the variable exponent Sobolev spaces, we establish the existence of a weak solution of this problem. Our results extend and generalize several corresponding results from the existing literature.
一类具有𝑝(1)-类拉普拉斯算子的Neumann边值问题的弱解
摘要研究了一类含有p≠(x) p(x) -类拉普拉斯算子的方程的Neumann边值问题弱解的存在性。利用广义(S +) (S_{+})型半连续算子的拓扑度理论和变指数Sobolev空间理论,建立了该问题弱解的存在性。我们的结果扩展和推广了现有文献的几个相应结果。
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