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›› 2019, Vol. 36 ›› Issue (1): 11-14.DOI: 10.7523/j.issn.2095-6134.2019.01.003

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Existence of positive solutions for a class of Kirchhoff-type equations with critical Hardy-Sobolev exponent

LI Hongying1, LIAO Jiafeng1,2   

  1. 1. School of Mathematics and Information, China West Normal University, Nanchong 63700;
    2. School of Mathematics, Zunyi Normal College, Zunyi 563006, Guizhou, China
  • Received:2017-05-08 Revised:2017-11-16 Online:2019-01-15

Abstract: he Kirchhoff-type equation with critical Hardy-Sobolev exponent is considered, where Ω⊂R3 is an open bounded domain with smooth boundary ∂Ω, 0∈Ω, a,b ≥ 0 and a+b>0, λ>0,0 < q < 1,0 ≤ s<1. The existence of its positive solutions is proved by using the variational methods.

Key words: Kirchhoff-type equation, critical Hardy-Sobolev exponent, positive solutions, variational method

CLC Number: