Infinitely many solutions for impulsive fractional differential equations through variational methods

Abstract

In this paper, we mainly consider the impulsive fractional differential equation. Under certain assumptions, some new criteria to guarantee the impulsive fractional impulsive fractional differential equation has infinitely many solutions are established. Moreover, we improve and extend some previous results.

Mathematics Subject Classification (2010):

• 34A08
• 34B37
• 35A15

Key words:

• Impulsive fractional differential equations
• variational methods
• critical point theory
• nontrivial solution
• infinitely many solutions

Notes

1 This work is supported by the NSFC (11571088, 11471109), the Zhejiang Provincial Natural Science Foundation of China (LY14A010024), and the Scientic Research Fund of the Hunan Provincial Education Department (14A098).