Existence of solutions for resonant double phase problems with mixed boundary value conditions

Yihao Yang (), Wulong Liu (), Patrick Winkert () and Xingye Yan ()
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Yihao Yang: Jiangxi University of Science and Technology
Wulong Liu: Jiangxi University of Science and Technology
Patrick Winkert: Technische Universität Berlin
Xingye Yan: Jiangxi University of Science and Technology

Partial Differential Equations and Applications, 2023, vol. 4, issue 3, 1-17

Abstract: Abstract We study a double phase problem with mixed boundary value conditions with reaction terms that resonate at the first eigenvalue of the related eigenvalue problem. Based on the maximum principle and homological local linking, we are going to prove the existence of at least two bounded nontrivial solutions for this problem.

Keywords: Double phase equation; Resonance; Mixed boundary conditions; Local linking; 35J15; 35J62; 35J92; 35P30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42985-023-00237-z

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