科研之友
微信
新浪微博
Facebook
分享链接
摘要
In this paper, we study the following Kirchhoff-type elliptic problem @@@ {-(a + b integral vertical bar del u vertical bar(2)dx)Delta u = lambda u(q-1) + mu u(2)*(-1), u > 0 in Omega, @@@ u= 0, on partial derivative Omega, @@@ where Omega subset of R-N(N >= 4) is a bounded domain with smooth boundary partial derivative Omega, a, b, lambda, mu > 0 and 1 < q < 2* = 2N/(N - 2). When N = 4, we obtain that there is a ground state solution to the problem for q is an element of (2, 4) by using a variational methods constrained on the Nehari manifold and also show the problem possesses infinitely many negative energy solutions for q is an element of (1, 2) by applying usual Krasnoselskii genus theory. In addition, we admit that there is a positive solution to the equations for N >= 5 under some suitable conditions.
- 出版日期2016-9-15
- 单位重庆大学
