A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum

Shaowei Chen and Haijun Zhou

Advances in Mathematical Physics, 2016, vol. 2016, issue 1

Abstract: We consider the nonlinear Schrödinger equation -Δu+f(u)=V(x)u in RN. The potential function V 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 nonlinearity f satisfies the resonance type condition lim|t|→∞f(t)/t = 0. Under some additional conditions on V and f, we prove that this equation has infinitely many solutions.

Date: 2016
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https://doi.org/10.1155/2016/3042493

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2016:y:2016:i:1:n:3042493

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