Journal of the
Korean Mathematical Society
JKMS

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

Copyright © The Korean Mathematical Society.

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