Perturbation from symmetry for indefinite semilinear elliptic equations |
| |
Authors: | Miguel Ramos Hossein Tehrani |
| |
Institution: | (1) CMAF, Faculty of Science, University of Lisbon, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal;(2) Department of Mathematical Sciences, University of Nevada, Las Vegas, NV 89154-4020, USA |
| |
Abstract: | We prove the existence of an unbounded sequence of solutions for an elliptic equation of the form \({-\Delta u=\lambda u + a(x)g(u)+f(x), u\in H^1_0(\Omega)}\), where \({\lambda \in \mathbb{R}, g(\cdot)}\) is subcritical and superlinear at infinity, and a(x) changes sign in Ω; moreover, g( ? s) = ? g(s) \({\forall s}\). The proof uses Rabinowitz’s perturbation method applied to a suitably truncated problem; subsequent energy and Morse index estimates allow us to recover the original problem. We consider the case of \({\Omega\subset \mathbb{R}^N}\) bounded as well as \({\Omega=\mathbb{R}^N, \, N\geqslant 3}\). |
| |
Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35J20 35J25 58E05 |
本文献已被 SpringerLink 等数据库收录! |
|