Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4664358 | Acta Mathematica Scientia | 2009 | 16 Pages |
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: {−Δpu − Δqu = |u|p*−2u+μ|u|r−2u in Ω,u|∂Ω = 0,where Ω ⊂ ℝN is a bounded domain, N > p, p* = NpN−p is the critical Sobolev exponent and μ > 0. We prove that 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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Li Gongbao, Zhang Guo,