Infinitely many solutions for nonlinear Schrödinger equations with slow decaying of potential

Liping Wang; Chunyi Zhao

doi:10.3934/dcds.2017071

Infinitely many solutions for nonlinear Schrödinger equations with slow decaying of potential

Liping Wang, Chunyi Zhao

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In the paper we prove the multiplicity existence of both nonlinear Schrödinger equation and Schrödinger system with slow decaying rate of electric potential at infinity. Namely, for any m;n > 0, the potentials P;Q have the asymptotic behavior {equation presented} then Schrödinger equation and Schrödinger system have infinitely many solutions with arbitrarily large energy, which extends the results of [37] for single Schrödinger equation and [30] for Schrödinger system.

Original language	English
Pages (from-to)	1707-1731
Number of pages	25
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	37
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2017071
State	Published - Mar 2017

Keywords

Finite dimension reduction
Nonlinear Schrödinger equations
Slow decaying

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10.3934/dcds.2017071

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abstract = "In the paper we prove the multiplicity existence of both nonlinear Schr{\"o}dinger equation and Schr{\"o}dinger system with slow decaying rate of electric potential at infinity. Namely, for any m;n > 0, the potentials P;Q have the asymptotic behavior \{equation presented\} then Schr{\"o}dinger equation and Schr{\"o}dinger system have infinitely many solutions with arbitrarily large energy, which extends the results of [37] for single Schr{\"o}dinger equation and [30] for Schr{\"o}dinger system.",

keywords = "Finite dimension reduction, Nonlinear Schr{\"o}dinger equations, Slow decaying",

author = "Liping Wang and Chunyi Zhao",

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language = "英语",

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AU - Wang, Liping

AU - Zhao, Chunyi

PY - 2017/3

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N2 - In the paper we prove the multiplicity existence of both nonlinear Schrödinger equation and Schrödinger system with slow decaying rate of electric potential at infinity. Namely, for any m;n > 0, the potentials P;Q have the asymptotic behavior {equation presented} then Schrödinger equation and Schrödinger system have infinitely many solutions with arbitrarily large energy, which extends the results of [37] for single Schrödinger equation and [30] for Schrödinger system.

AB - In the paper we prove the multiplicity existence of both nonlinear Schrödinger equation and Schrödinger system with slow decaying rate of electric potential at infinity. Namely, for any m;n > 0, the potentials P;Q have the asymptotic behavior {equation presented} then Schrödinger equation and Schrödinger system have infinitely many solutions with arbitrarily large energy, which extends the results of [37] for single Schrödinger equation and [30] for Schrödinger system.

KW - Finite dimension reduction

KW - Nonlinear Schrödinger equations

KW - Slow decaying

UR - https://www.scopus.com/pages/publications/85006999815

U2 - 10.3934/dcds.2017071

DO - 10.3934/dcds.2017071

M3 - 文章

AN - SCOPUS:85006999815

SN - 1078-0947

VL - 37

SP - 1707

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 3

ER -

Infinitely many solutions for nonlinear Schrödinger equations with slow decaying of potential

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Keywords

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