SPIKE LAYER SOLUTIONS FOR A SINGULARLY PERTURBED NEUMANN PROBLEM: VARIATIONAL CONSTRUCTION WITHOUT A NONDEGENERACY

被引：0
|
作者：
Byeon, Jaeyoung [1 ]
Moon, Sang-Hyuck [1 ]
机构：
[1] Korea Adv Inst Sci & Technol, Dept Math Sci, 291 Daehak Ro, Daejeon 34141, South Korea
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2019年 / 18卷 / 04期
基金：
新加坡国家研究基金会;
关键词：
Singular perturbation; Neumann condition; spike layer; mean curvature; transplantation flow; gradient flow; variational; LEAST-ENERGY SOLUTIONS; NONLINEAR SCHRODINGER-EQUATIONS; POSITIVE SOLUTIONS; MULTIPEAK SOLUTIONS; ELLIPTIC PROBLEMS; STANDING WAVES; PEAK SOLUTIONS; BERESTYCKI; UNIQUENESS; EXISTENCE;
D O I：
10.3934/cpaa.2019089
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the following singularly perturbed problem epsilon(2)Delta u - u + f(u) = 0, u > 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega. Existence of a solution with a spike layer near a min-max critical point of the mean curvature on the boundary partial derivative Omega is well known when a nondegeneracy for a limiting problem holds. In this paper, we use a variational method for the construction of such a solution which does not depend on the nondengeneracy for the limiting problem. By a purely variational approach, we construct the solution for an optimal class of nonlinearities f satisfying the Berestycki-Lions conditions.
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页码：1921 / 1965
页数：45
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