Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610452 | Journal of Differential Equations | 2014 | 53 Pages |
Abstract
In this paper the question of finding infinitely many solutions to the problem −Δu+a(x)u=|u|p−2u−Δu+a(x)u=|u|p−2u, in RNRN, u∈H1(RN)u∈H1(RN), is considered when N≥2N≥2, p∈(2,2N/(N−2))p∈(2,2N/(N−2)), and the potential a(x)a(x) is a positive function which is not required to enjoy symmetry properties. Assuming that a(x)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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Giovanna Cerami, Riccardo Molle, Donato Passaseo,