Infinitely many solutions for fractional Schr\"odinger equations in R^N
Using variational methods we prove the existence of infinitely many solutions to the fractional Schrodinger equation $$ (-\Delta)^su+V(x)u=f(x,u), \quad x\in\mathbb{R}^N, $$ where $N\ge 2, s\in (0,1)$. $(-\Delta)^s$ stands for the fractional Laplacian. The potential function satisfies $V(x...
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doaj-5820220b6af44daabf0b87be970fde0b2020-11-25T01:18:36ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-03-01201688,115Infinitely many solutions for fractional Schr\"odinger equations in R^NCaisheng Chen0 Hohai Univ., Nanjing, China Using variational methods we prove the existence of infinitely many solutions to the fractional Schrodinger equation $$ (-\Delta)^su+V(x)u=f(x,u), \quad x\in\mathbb{R}^N, $$ where $N\ge 2, s\in (0,1)$. $(-\Delta)^s$ stands for the fractional Laplacian. The potential function satisfies $V(x)\geq V_0>0$. The nonlinearity f(x,u) is superlinear, has subcritical growth in u, and may or may not satisfy the (AR) condition.http://ejde.math.txstate.edu/Volumes/2016/88/abstr.htmlFractional Schrodinger equation variational methods(PS) condition(C)c condition |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Caisheng Chen |
spellingShingle |
Caisheng Chen Infinitely many solutions for fractional Schr\"odinger equations in R^N Electronic Journal of Differential Equations Fractional Schrodinger equation variational methods (PS) condition (C)c condition |
author_facet |
Caisheng Chen |
author_sort |
Caisheng Chen |
title |
Infinitely many solutions for fractional Schr\"odinger equations in R^N |
title_short |
Infinitely many solutions for fractional Schr\"odinger equations in R^N |
title_full |
Infinitely many solutions for fractional Schr\"odinger equations in R^N |
title_fullStr |
Infinitely many solutions for fractional Schr\"odinger equations in R^N |
title_full_unstemmed |
Infinitely many solutions for fractional Schr\"odinger equations in R^N |
title_sort |
infinitely many solutions for fractional schr\"odinger equations in r^n |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
2016-03-01 |
description |
Using variational methods we prove the existence of infinitely
many solutions to the fractional Schrodinger equation
$$
(-\Delta)^su+V(x)u=f(x,u), \quad x\in\mathbb{R}^N,
$$
where $N\ge 2, s\in (0,1)$. $(-\Delta)^s$ stands for the fractional
Laplacian. The potential function satisfies $V(x)\geq V_0>0$.
The nonlinearity f(x,u) is superlinear, has subcritical
growth in u, and may or may not satisfy the (AR) condition. |
topic |
Fractional Schrodinger equation variational methods (PS) condition (C)c condition |
url |
http://ejde.math.txstate.edu/Volumes/2016/88/abstr.html |
work_keys_str_mv |
AT caishengchen infinitelymanysolutionsforfractionalschrodingerequationsinrn |
_version_ |
1725141660044623872 |