Acta mathematica scientia, Series B >
MULTIPLE SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL EXPONENT
Received date: 2008-12-31
Online published: 2009-07-20
Supported by
Partially supported by NSFC (10571069 and 10631030), and the Lab of Mathematical Sciences, CCNU, Hubei Province, China
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 ⊂ RN is a bounded domain, N > p, p* = Np /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.
Key words： p&q-Laplacian; multiplicity of solutions; critical exponent
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 . DOI: 10.1016/S0252-9602(09)60077-1
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