scholarly journals Singularly perturbed semilinear Neumann problem with non-normally hyperbolic critical manifold

2010 ◽  
pp. 1-11
Author(s):  
Robert Vrabel
Keyword(s):  
Neumann Problem ◽  
Singularly Perturbed ◽  
Critical Manifold

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

2009 ◽  
Vol 139 (2) ◽  
pp. 427-448 ◽  
Author(s):  
Chunyi Zhao
Keyword(s):  
Positive Integer ◽  
Neumann Problem ◽  
Smooth Function ◽  
Local Minimum ◽  
Singularly Perturbed ◽  
Minimum Point ◽  
Local Minimum Point ◽  
Image Position

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 K ≤ K(ε), there always exists a solution with K interior peaks concentrating at a strict sth-order local minimum point of a.

scholarly journals On Finding Multiple Solutions to a Singularly Perturbed Neumann Problem

2012 ◽  
Vol 34 (1) ◽  
pp. A395-A420 ◽  
Author(s):  
Ziqing Xie ◽  
Yongjun Yuan ◽  
Jianxin Zhou
Keyword(s):  
Neumann Problem ◽  
Multiple Solutions ◽  
Singularly Perturbed

ON A SINGULARLY PERTURBED NEUMANN PROBLEM WITH THE CRITICAL EXPONENT

2001 ◽  
Vol 26 (11-12) ◽  
pp. 1929-1946 ◽  
Author(s):  
Nassif Ghoussoub ◽  
Changfeng Gui ◽  
Meijun Zhu
Keyword(s):  
Critical Exponent ◽  
Neumann Problem ◽  
Singularly Perturbed
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