Multiplicity of positive and nodal solutions for scalar field equations |
| |
Authors: | Giovanna Cerami Riccardo Molle Donato Passaseo |
| |
Affiliation: | 1. Dipartimento di Matematica, Politecnico di Bari, Via Amendola no. 126/B, 70126 Bari, Italy;2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica no. 1, 00133 Roma, Italy;3. Dipartimento di Matematica “E. De Giorgi”, Università di Lecce, P.O. Box 193, 73100 Lecce, Italy |
| |
Abstract: | In this paper the question of finding infinitely many solutions to the problem −Δu+a(x)u=|u|p−2u, in RN, u∈H1(RN), is considered when N≥2, p∈(2,2N/(N−2)), and the potential a(x) is a positive function which is not required to enjoy symmetry properties. Assuming that a(x) satisfies a suitable “slow decay at infinity” condition and, moreover, that its graph has some “dips”, we prove that the problem admits either infinitely many nodal solutions or infinitely many constant sign solutions. The proof method is purely variational and allows to describe the shape of the solutions. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|