Infinitely many solutions for double phase problem with unbounded potential in RN. (January 2022)

• Record Type: Journal Article
• Authors: Stegliński, Robert
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: 35J60 -- 35D30 -- 35J20; Double phase problems -- Musielak–Orlicz–Sobolev spaces -- Fountain Theorem -- Dual Fountain Theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112580
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a double phase problem in R N − div ( | ∇ u | p − 2 ∇ u + a ( x ) | ∇ u | q − 2 ∇ u ) + V ( x ) ( | u | p − 2 u + a ( x ) | u | q − 2 u ) = f ( x, u ) with an unbounded potential V and reaction term f, which does not satisfy the Ambrosetti–Rabinowitz condition. A new functional setting was provided for this problem. Using the Fountain and Dual Fountain Theorem with Cerami condition, we obtain some existence of infinitely many solutions. Our result extends some recent work in the literature.