# Journal of theKorean Mathematical SocietyJKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

## Article

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J. Korean Math. Soc. 2020; 57(4): 825-844

Published online July 1, 2020 https://doi.org/10.4134/JKMS.j190368

## Infinitely many solutions for fractional Schr\"odinger equation with superquadratic conditions or combined nonlinearities

Mohsen Timoumi

Faculty of Sciences of Monastir

### Abstract

We obtain infinitely many solutions for a class of fractional Schr\"odinger equation, where the nonlinearity is superquadratic or involves a combination of superquadratic and subquadratic terms at infinity. By using some weaker conditions, our results extend and improve some existing results in the literature.

Keywords: Fractional Schr\"odinger equation, infinitely many solutions, variational methods, superlinear conditions, combined nonlinearities

MSC numbers: Primary 35A15, 35J60, 35R11 47G20

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