Ground states for nonlinear Schrödinger equation with sign-changing and vanishing potential

Xue, Ye; Han, Zhiqing; Guo, Xiaojie

doi:10.1080/17476933.2021.1988582

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2022

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“…For (1.1) with sign-changing and vanishing potentials V (x), Wang and Zhou [22] and Xue et al [25] deal with the existence of ground states based on monotonicity and some other proper conditions, respectively.…”

Section: Introductionmentioning

confidence: 99%

Ground States of Nonlocal Fractional Schrödinger Equations with Potentials Well

Xue

Wei

2022

Taiwanese J. Math.

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Inspired by Alves and Souto [2], we investigate the existence of nontrivial solutions to a class of fractional Schrödinger equations with potentials well. Taking the superlinear nonlinearities into consideration, we obtain the existence of nontrivial solutions by loosing monotonicity. Furthermore, a ground state solution is established. This was proved in [7] that (1.1) can be reduced to the classical Schrödinger equation, since (− ) s can be changed to the standard Laplace − as s → 1.

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Section: Introductionmentioning

confidence: 99%