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On the number of interior peaks of solutions to a non-autonomous singularly perturbed Neumann problem

Published online by Cambridge University Press:  25 March 2009

Chunyi Zhao
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200062, People's Republic of China (chunyi_zhao@yahoo.com)

Abstract

We study the following non-autonomous singularly perturbed Neumann problem:

where the index p is subcritical and a(x) is a positive smooth function in . We show that, given ε small enough, there exists a K(ε) such that, for any positive integer KK(ε), there always exists a solution with K interior peaks concentrating at a strict sth-order local minimum point of a.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2009

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