Existence of radial solutions with prescribed number of zeros for elliptic equations and their Morse index |
| |
Authors: | Abdellaziz Harrabi Abdelbaki Selmi |
| |
Institution: | a Institut de Mathématiques Appliquées et d?Informatiques, Kairouan, Tunisia b Département de Mathématiques, Faculté des Sciences de Tunis, Université Elmanar, Campus Universitaire 2092, Tunis, Tunisia c Département de Mathématiques, Faculté des Sciences de Bizerte, Zarzouna 7021, Bizerte, Tunisia |
| |
Abstract: | In this paper we consider radially symmetric solutions of the nonlinear Dirichlet problem Δu+f(|x|,u)=0 in Ω, where Ω is a ball in RN, N?3 and f satisfies some appropriate assumptions. We prove existence of radially symmetric solutions with k prescribed number of zeros. Moreover, when f(|x|,u)=K(|x|)|u|p−1u, using the uniqueness result due to Tanaka (2008) 21], we verify that these solutions are non-degenerate and we prove that their radial Morse index is exactly k. |
| |
Keywords: | 35J60 35J65 58E05 |
本文献已被 ScienceDirect 等数据库收录! |
|