MULTIPLE SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL EXPONENT

doi:10.1016/S0252-9602(09)60077-1

摘要/Abstract

摘要：

In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p&q-Laplacian type involving the critical Sobolev exponent:

−△_pu − △_qu = |u|^p*−2u + μ|u|^r−2u in Ω,
u|∂Ω= 0,

where Ω ⊂ R^N is a bounded domain, N > p, p* = N_p /N−p is the critical Sobolev exponent and μ > 0. We prove that if 1 < r < q < p < N, then there is a μ₀ > 0, such that for any μ ∈ (0, μ₀), the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem.

关键词: p&q-Laplacian, multiplicity of solutions, critical exponent

Abstract:

In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p&q-Laplacian type involving the critical Sobolev exponent:

−△_pu − △_qu = |u|^p*−2u + μ|u|^r−2u in Ω,
u|∂Ω= 0,

Key words: p&q-Laplacian, multiplicity of solutions, critical exponent

中图分类号:

35J60

李工宝, 张国. MULTIPLE SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL EXPONENT[J]. 数学物理学报(英文版), 2009, 29(4): 903-918.

LI Gong-Bao, ZHANG Guo. MULTIPLE SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL EXPONENT[J]. Acta mathematica scientia,Series B, 2009, 29(4): 903-918.

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