A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum. (2nd March 2016)

• Record Type: Journal Article
• Authors: Chen, Shaowei; Zhou, Haijun
• Other Names: Bellazzini Jacopo Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2016(2016)
• Publication Date: 2016-03-02
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2016/3042493
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : We consider the nonlinear Schrödinger equation- Δ u + f ( u ) = V ( x ) u i n R N . The potential functionV satisfies that the essential spectrum of the Schrödinger operator- Δ - V is[ 0, + ∞ ) and this Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. The nonlinearityf satisfies the resonance type conditionl i m t → ∞ f ( t ) / t = 0 . Under some additional conditions onV andf, we prove that this equation has infinitely many solutions.