Resonant double phase equations. (April 2022)

• Record Type: Journal Article
• Authors: Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Zhang, Youpei
• Is Part Of: Nonlinear analysis. Volume 64(2022)
• Publication Date: 2022-04
• Subjects: Double phase equation -- Unbalanced growth -- Musielak–Orlicz–Sobolev spaces -- Maximum principle -- Resonance -- Critical groups; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103454
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider a double phase Dirichlet equation with a reaction which is asymptotically as x → ± ∞, resonant with respect to the first eigenvalue of a related eigenvalue problem. Using variational tools together with Morse theoretic arguments, we prove the existence of at least two bounded nontrivial solutions for the problem.