Least energy solutions to semi-linear elliptic problems on metric graphs

被引：9

作者：

Kurata, Kazuhiro ^{[1
]}

Shibata, Masataka ^{[2
]}

机构：

[1] Tokyo Metropolitan Univ, Dept Math Sci, 1-1 Minami Osawa, Hachioji, Tokyo 1920397, Japan

[2] Tokyo Inst Technol, Dept Math, Meguro Ku, 2-12-1 Oh Okayama, Tokyo 1528551, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 491卷 / 01期

关键词：

Metric graph; Variational method; Least energy solution; NONLINEAR SCHRODINGER-EQUATIONS; GROUND-STATES;

D O I：

10.1016/j.jmaa.2020.124297

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider positive solutions of semi-linear elliptic equations -epsilon(2)Delta u + u = u(p) on compact metric graphs, where 1 < p < infinity. For each epsilon > 0, there exists a least energy positive solution u(epsilon). We focus on the asymptotic behavior of u(epsilon) and show that u(epsilon) has exactly one local maximum point x(epsilon) and concentrates like a peak for sufficiently small epsilon. Moreover, we prove that the location of x(epsilon) is determined by the length of edges of graphs. These results are shown for the more general super-linear term f(u) instead of u(p). (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：22