Local uniqueness for the multi-bump solutions to the problem of Ambrosetti

Local uniqueness for the multi-bump solutions to the problem of Ambrosetti–Prodi type

Published:2022-04-01 Issue:4 Volume:63 Page:041512
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:J. Math. Phys.

Author:

Chen Haixia¹^ORCID,Chen Mengyao²^ORCID,Li Qi²^ORCID

Affiliation:

1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, People’s Republic of China

2. College of Science and Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430065, People’s Republic of China

Abstract

We consider a type of elliptic problem of Ambrosetti–Prodi type with the subcritical Sobolev exponent. Based on the local type of Pohozaev identities, we prove the uniqueness for multi-bump solutions constructed by Dancer and Yan [J. Differ. Equations 210, 317–351 (2005)]. As a consequence, we obtain the local uniqueness for the problem of Ambrosetti–Prodi type.

Funder

National Natural Science Foundation of China

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://aip.scitation.org/doi/pdf/10.1063/5.0065173

Reference37 articles.

1. The exact number of solutions for a class of ordinary differential equations through Morse Index computation

2. Radially symmetric solutions to a superlinear Dirichlet problem in a ball with jumping nonlinearities

3. Uniqueness of positive solutions of Δu−u+up=0 in Rn

4. On a conjecture related to the number of solutions of a nonlinear Dirichlet problem

5. Multiplicity results for an ode problem with even nonlinearity

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Ground state solution for fractional problem with critical combined nonlinearities;Electronic Journal of Qualitative Theory of Differential Equations;2023