Electron. J. Differential Equations, Vol. 2022 (2022), No. 55, pp. 1-10.

Double phase equations with an indefinite concave term

Zhenhai Liu, Nikolaos S. Papageorgiou

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.

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Zhenhai Liu
Guangxi Colleges and Universities
Key Laboratory of Complex System Optimization and Big Data Processing
Yulin Normal University
Yulin 537000, China
email: zhhliu@hotmail.com
  Nikolaos S. Papageorgiou
Department of Mathematics
National Technical University
Zografou Campus, 15780 Athens, Greece
email: npapg@math.ntua.gr

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