Multiplicity of positive solutions for quasilinear elliptic equations involving critical nonlinearity
发布时间：2020-06-01
点击次数：
- 论文类型：
- 期刊论文
- 发表时间：
- 2020-01-01
- 发表刊物：
- ADVANCES IN NONLINEAR ANALYSIS
- 收录刊物：
- SCIE
- 文献类型：
- J
- 卷号：
- 9
- 期号：
- 1
- 页面范围：
- 1420-1436
- ISSN号：
- 2191-9496
- 关键字：
- Quasilinear elliptic equation; Positive solution; Nehari manifold
- 摘要：
- We are concerned with the following quasilinear elliptic equation
-Delta u -Delta(u(2))u =mu vertical bar u vertical bar(q-2)u +vertical bar u vertical bar(2.2*-2)u, u is an element of H-0(1)(Omega), (QSE)
where Omega subset of R-N is a bounded domain, N >= 3, q(N) < q < 2.2* , 2* = 2N/(N- 2), q(N) = 4 for N >= 6 and q(N) = 2(N+2)/N-2 for N = 3, 4, 5, and y is a positive constant. By employing the Nehari manifold and the Lusternik-Schnirelman category theory, we prove that there exists mu* > 0 such that (QSE) admits at least cat(Omega)(Omega) positive solutions when mu is an element of (0, mu*).
- 第一作者
- Fang, Xiangdong
- 合写作者
- Zhang, Jianjun
- 通讯作者
- Fang, XD (reprint author), Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.