Infinitely many positive solutions for a nonlocal problem with competing potentials

Abstract

Abstract The present paper deals with a class of nonlocal problems. Under some suitable assumptions on the decay rate of the coefficients, we derive the existence of infinitely many positive solutions to the problem by applying reduction method. Comparing to the previous work, we encounter some new challenges because of competing potentials. By doing some delicate estimates for the competing potentials, we overcome the difficulties and find infinitely many positive solutions.

Keywords

• Competing potentials
• Infinitely many solutions
• Lyapunov–Schmidt reduction