MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES AND MULTIPLE HARDY-TYPE TERMS

doi:10.1016/S0252-9602(13)60084-3

摘要/Abstract

摘要：

In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem
−Δ_pu −∑^k_i₌₁μ_i|u|^p−2/|x − a_i|_p u = |u|^p*−2u + λ|u|^q−2u, x ∈Ω,
where Ω （R^N(N ≥3) is a smooth bounded domain such that the different points a_i∈ Ω, i = 1, 2, · · · , k, 0 ≤ μ_i < ¯μ = (N−p/p )^p, λ > 0, 1 ≤ q < p, and p^* = p^N/N−p . The results depend crucially on the parameters λ, q and μi for i = 1, 2, · · · , k.

关键词: multiple positive solutions, concave-convex nonlinearities, multiple Hardy-type terms

Abstract:

Key words: multiple positive solutions, concave-convex nonlinearities, multiple Hardy-type terms

中图分类号:

35J61

Tsing-San HSU. MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES AND MULTIPLE HARDY-TYPE TERMS[J]. 数学物理学报(英文版), 2013, 33(5): 1314-1328.

Tsing-San HSU. MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES AND MULTIPLE HARDY-TYPE TERMS[J]. Acta mathematica scientia,Series B, 2013, 33(5): 1314-1328.

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