A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum. (2nd March 2016) - Chen, Shaowei; Zhou, Haijun
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.