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›› 2012, Vol. 29 ›› Issue (5): 577-585.DOI: 10.7523/j.issn.2095-6134.2012.5.001

• Research Articles •     Next Articles

Multiple positive solutions for a three-dimensional Kirchhoff-type problem with a Hardy term

LIU Xing, SUN Yi-Jing   

  1. School of Mathematics, Graduate University, Chinese Academy of Sciences, Beijing 100049, China
  • Received:2011-05-09 Revised:2011-07-04 Online:2012-09-15

Abstract:

We investigate the following three-dimensional Kirchhoff-type problem
where Ω is a smooth bounded domain in R3, 0∈Ω, 0 < q < 1, 0 ≤ s < 1, 4 < p < 2*(s)=2(3-s), parameters a,b,λ > 0. We have established the existence of multiple positive solutions to the problem by using variational methods.

Key words: Kirchhoff-type problem, Hardy term, Nehari manifold, positive solutions

CLC Number: