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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