Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 55, pp. 1-10.

Title: Double phase equations with an indefinite concave term
       
Authors: Zhenhai Liu (Guangxi Minzu Univ., Nanning, Guangxi, 530006, China)
         Nikolaos S. Papageorgiou (National Technical Univ., Athens, Greece)

Abstract:  
We consider a Dirichlet problem having a double phase differential
operator with unbalanced growth and reaction involving the combined
effects of a concave (sublinear) and of a convex (superlinear) terms.
We allow the coefficient $\mathcal E\in L^\infty(\Omega)$ of the concave
term to be sign changing. We show that when $\|\mathcal E\|_\infty $
is small the problem has at least two bounded positive solutions.

Submitted January 12, 2022. Published July 28, 2022.
Math Subject Classifications: 35J75, 35J20, 35J60.
Key Words: Unbalanced growth; generalized Orlicz spaces; positive solution;
           concave-convex problem; mountain pass theorem.