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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 15
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Articles

Multiple sign-changing solutions for nonlinear Schrödinger equations with potential well

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Pages 2555-2570 | Received 30 Oct 2018, Accepted 16 Dec 2018, Published online: 30 Jan 2019
 

Abstract

We study the existence of sign-changing solutions for the following nonlinear Schrödinger equation Δu+Vλ(x)u=f(x,u),xRN, where the potential Vλ(x) has a potential well with bottom independent of the parameter λ>0. We show that as λ+ more and more sign-changing solutions of the nonlinear Schrödinger equation exist. The solutions lie in H1(RN) and are localized near the bottom of the potential well, but not near local minima of the potential.

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No potential conflict of interest was reported by the authors.

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