Infinitely many positive solutions for a double phase problems involving the double phase operator - Lian, Chunbo; Ge, Bin; Cao, Qinghai; Zhang, Yu (Topological Methods in Nonlinear Analysis, 2024)
In this paper we study a double phase problem which involves the double phase operator, and thenonlinear term has an oscillatory behavior.By using variational methods and the theory ofthe Musielak-Orlicz-Sobolev space, we establish theexistence of infinitely many solutions whose $W_0^{1,H}(Ω)$-norms tend to zero (to infinity, respectively) whenever the nonlinearity oscillates at zero (at infinity, respectively).