Infinitely many positive solutions for a double phase problem

Abstract

Abstract This paper is concerned with the existence of infinitely many positive solutions to a class of double phase problem. By variational methods and the theory of the Musielak–Orlicz–Sobolev space, we establish the existence of infinitely many positive solutions whose W 0 1 , H ( Ω ) $W_{0}^{1,H}(\varOmega )$ -norms and L ∞ $L^{\infty }$ -norms tend to zero under suitable hypotheses about nonlinearity.

Keywords

• Double phase operator
• Multiple solutions
• Variational methods