Revista Matemática Iberoamericana


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Volume 23, Issue 3, 2007, pp. 1039–1066
DOI: 10.4171/RMI/523

Published online: 2007-12-31

A new type of solutions for a singularly perturbed elliptic Neumann problem

Gongbao Li[1], Shuangjie Peng[2] and Shusen Yan[3]

(1) Huazhong Normal University, Wuhan, China
(2) Central China Normal University, Wuhan, China
(3) University of New England, Armidale, Australia

We prove the existence of positive solutions concentrating simultaneously on some higher dimensional manifolds near and on the boundary of the domain for a nonlinear singularly perturbed elliptic Neumann problem.

Keywords: Singularly perturbed elliptic equation; variational method, concentrating solutions, higher dimensional manifolds

Li Gongbao, Peng Shuangjie, Yan Shusen: A new type of solutions for a singularly perturbed elliptic Neumann problem. Rev. Mat. Iberoamericana 23 (2007), 1039-1066. doi: 10.4171/RMI/523