Some Results for a Class of Kirchhoff-Type Problems with Hardy-Sobolev Critical Exponent

被引:0
作者
Li, Hong-Ying [1 ]
Pu, Yang [1 ]
Liao, Jia-Feng [1 ,2 ]
机构
[1] China West Normal Univ, Sch Math & Informat, Nanchong 637002, Sichuan, Peoples R China
[2] China West Normal Univ, Coll Math Educ, Nanchong 637002, Sichuan, Peoples R China
关键词
Kirchhoff-type problems; Hardy-Sobolev critical exponent; positive solution; variational method; MULTIPLE POSITIVE SOLUTIONS; SEMILINEAR ELLIPTIC-EQUATIONS; SIGN-CHANGING SOLUTIONS; EXISTENCE; TERM;
D O I
10.1007/s00009-019-1349-3
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study a class of Kirchhoff equations {-(a + b integral(Omega)vertical bar del u vertical bar(2) dx) Delta u = u(3)/vertical bar x vertical bar + lambda u(q), in Omega, u = 0, on partial derivative Omega, where Omega subset of R-3 is a bounded domain with smooth boundary and 0 is an element of Omega, a, b, lambda > 0, 0 < q < 1. By the variational method, two positive solutions are obtained. Moreover, when b > 1/A(1)(2) (A(1) > 0 is the best Sobolev-Hardy constant), using the critical point theorem, infinitely many pairs of distinct solutions are obtained for any lambda > 0.
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页数:16
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