Zhenhai Liu, Nikolaos S. Papageorgiou
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
of the concave
term to be sign changing. We show that when
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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DOI: https://doi.org/10.58997/ejde.2022.55
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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 |
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| Nikolaos S. Papageorgiou Department of Mathematics National Technical University Zografou Campus, 15780 Athens, Greece email: npapg@math.ntua.gr |
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