A NOTE ON THE UNIQUENESS AND THE NON-DEGENERACY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS AND ITS APPLICATION

doi:10.1016/S0252-9602(18)30803-8

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (4): 1121-1142.doi: 10.1016/S0252-9602(18)30803-8

A NOTE ON THE UNIQUENESS AND THE NON-DEGENERACY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS AND ITS APPLICATION

Shinji ADACHI¹, Masataka SHIBATA², Tatsuya WATANABE³

1. Department of Mathematical and Systems Engineering, Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu 432-8561, Japan;
2. Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan;
3. Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan

收稿日期:2017-02-10 修回日期:2018-05-01 出版日期:2018-08-25 发布日期:2018-08-25
通讯作者: Shinji ADACHI,E-mail:adachi@shizuoka.ac.jp E-mail:adachi@shizuoka.ac.jp
作者简介:Masataka SHIBATA,E-mail:shibata@math.titech.ac.jp;Tatsuya WATANABE,E-mail:tatsuw@cc.kyoto-su.ac.jp
基金资助:
The third author is supported by JSPS Grant-in-Aid for Scientific Research (C) (15K04970).

A NOTE ON THE UNIQUENESS AND THE NON-DEGENERACY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS AND ITS APPLICATION

Shinji ADACHI¹, Masataka SHIBATA², Tatsuya WATANABE³

1. Department of Mathematical and Systems Engineering, Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu 432-8561, Japan;
2. Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan;
3. Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan

Received:2017-02-10 Revised:2018-05-01 Online:2018-08-25 Published:2018-08-25
Contact: Shinji ADACHI,E-mail:adachi@shizuoka.ac.jp E-mail:adachi@shizuoka.ac.jp
Supported by:
The third author is supported by JSPS Grant-in-Aid for Scientific Research (C) (15K04970).

摘要/Abstract

摘要：

In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE analysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified Schrödinger equations.

关键词: positive radial solution, uniqueness, non-degeneracy, shooting method

Abstract:

Key words: positive radial solution, uniqueness, non-degeneracy, shooting method

Shinji ADACHI, Masataka SHIBATA, Tatsuya WATANABE. A NOTE ON THE UNIQUENESS AND THE NON-DEGENERACY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS AND ITS APPLICATION[J]. 数学物理学报(英文版), 2018, 38(4): 1121-1142.

Shinji ADACHI, Masataka SHIBATA, Tatsuya WATANABE. A NOTE ON THE UNIQUENESS AND THE NON-DEGENERACY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS AND ITS APPLICATION[J]. Acta mathematica scientia,Series B, 2018, 38(4): 1121-1142.

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A NOTE ON THE UNIQUENESS AND THE NON-DEGENERACY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS AND ITS APPLICATION

A NOTE ON THE UNIQUENESS AND THE NON-DEGENERACY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS AND ITS APPLICATION

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