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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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| Authors: | Shinji ADACHI Masataka SHIBATA Tatsuya WATANABE |
| Affiliation: | Department of Mathematical and Systems Engineering, Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu 432-8561, Japan;Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan;Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan |
| 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. |
| Keywords: | positive radial solution uniqueness non-degeneracy shooting method 35J61 35A02 35B05 |
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