A Multiplicity Theorem for Superlinear Double Phase Problems

Abstract

We consider a nonlinear Dirichlet problem driven by the double phase differential operator and with a superlinear reaction which need not satisfy the Ambrosetti–Rabinowitz condition. Using the Nehari manifold, we show that the problem has at least three nontrivial bounded solutions: nodal, positive and by the symmetry of the behaviour at +∞ and −∞ also negative.

Keywords

• double phase operator
• Nehari manifold
• superlinear reaction
• constant sign and nodal solutions
• Musielak–Orlicz spaces