期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 491, 期 1, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2020.124297
关键词
Metric graph; Variational method; Least energy solution
资金
- JSPS KAKENHI [18K03356, 18K03362, 17H01092, 19K03587]
- Grants-in-Aid for Scientific Research [19K03587, 18K03356, 18K03362, 17H01092] Funding Source: KAKEN
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.
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