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Multiple existence of solutions for a singularly perturbed nonlinear elliptic problem on a Riemannian manifold

Published online by Cambridge University Press:  30 January 2012

Norimichi Hirano
Norimichi Hirano
Affiliation:
Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, Tokiwadai, Hodogayaku, Yokohama, Japan (hirano@math.sci.ynu.ac.jp)
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Abstract

Let (M, g) be a compact smooth N-dimensional Riemannian manifold without boundary. We consider the multiple existence of positive solutions of the problem

where Δg stands for the Laplacian in M and f ε C2(M).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 1 , February 2012 , pp. 81 - 114
Copyright
Copyright © Royal Society of Edinburgh 2012

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