MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS

被引：0
|
作者：
Chen, Wenjing [1 ]
Yang, Jianfu [1 ]
机构：
[1] Jiangxi Normal Univ, Dept Math, Nanchang 330022, Jiangxi, Peoples R China
来源：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年
关键词：
Multiple solutions; Semilinear elliptic equation; Riemannian manifold; Ljusternik-Schnirelmann category; SCALAR FIELD-EQUATIONS; SCHRODINGER-EQUATIONS; POSITIVE SOLUTIONS; EXISTENCE; STATES;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let (M, g) be a compact, connected, orientable, Riemannian n-manifold of class C-infinity with Riemannian metric g (n >= 3). We study the existence of solutions to the equation -epsilon(2)Delta(g)u + V(x)u = K(x)vertical bar u vertical bar(p-2)u on this Riemannian manifold. Here 2 < p < 2* = 2n/(n - 2), V (x) and K(x) are continuous functions. We show that the shape of V (x) and K(x) affects the number of solutions, and then prove the existence of multiple solutions.
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页数：16
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