数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (5): 1314-1328.doi: 10.1016/S0252-9602(13)60084-3

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

Tsing-San HSU   

  1. Center for General Education, Chang Gung University, Kwei-Shan, Tao-Yuan 333, Taiwan, China
  • 收稿日期:2011-11-14 出版日期:2013-09-20 发布日期:2013-09-20

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

Tsing-San HSU   

  1. Center for General Education, Chang Gung University, Kwei-Shan, Tao-Yuan 333, Taiwan, China
  • Received:2011-11-14 Online:2013-09-20 Published:2013-09-20

摘要:

In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem
−Δpu −∑ki=1μi|u|p−2/|xai|p u = |u|p*−2uλ|u|q−2u,      ∈Ω,
where Ω (RN(N ≥3) is a smooth bounded domain such that the different points ai ∈ Ω, i = 1, 2, · · · , k, 0 ≤ μi < ¯μ = (Np/p )pλ > 0, 1 ≤ q < p, and p* = pN/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:

In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem
−Δpu −∑ki=1μi|u|p−2/|xai|p u = |u|p*−2uλ|u|q−2u,      ∈Ω,
where Ω (RN(N ≥3) is a smooth bounded domain such that the different points ai ∈ Ω, i = 1, 2, · · · , k, 0 ≤ μi < ¯μ = (Np/p )pλ > 0, 1 ≤ q < p, and p* = pN/N−p . The results depend crucially on the parameters λ, q and μi for i = 1, 2, · · · , k.

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

中图分类号: 

  • 35J61