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

Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (4): 1121-1142.doi: 10.1016/S0252-9602(18)30803-8

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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).

Abstract

Abstract:

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.

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].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

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