一类带有Neumann边值条件的拟线性椭圆外部问题的多解性

Abstract

Abstract:

In this paper, we consider the following quasi-linear elliptic exterior problem with Neumann boundary value conditions

where Ω is a smooth exterior domain of the Euclidean space(R^N,|·|)(N ≥ 3), and n is the unit vector of the outward normal on the boundary ∂Ω. λ is a positive parameter, 1< p< N, 1< q< p< r< p^*, p^*=Np/(N-p). By the mountain-pass theorem and Ekeland's variational principle, we establish the existence of two solutions for this problem when functions a(x), b(x), h₁(x), h₂(x) and g(x) satisfy certain conditions.

Key words: Mountain-pass Theorem, Variational methods, Neumann boundary conditions

CLC Number:

O175.23

Song Hongxue, Yan Qinglun. Multiple Solutions for Quasilinear Elliptic Exterior Problem with Neumann Boundary Conditions[J].Acta mathematica scientia,Series A, 2015, 35(5): 845-854.

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Multiple Solutions for Quasilinear Elliptic Exterior Problem with Neumann Boundary Conditions

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