Infinitely many solutions for a generalized p(·)‐Laplace equation involving Leray–Lions type operators. (4th February 2021)

• Record Type: Journal Article
• Authors: Hai Ha, Hoang; Ho, Ky; Sim, Inbo
• Other Names: Alaoui Mohammed Kbiri guestEditor.; Messaoudi Salim guestEditor.; Hästö Peter guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 14(2022)
• Page Start: 8450
• Page End: 8473
• Publication Date: 2021-02-04
• Subjects: a priori bound -- p(·)‐Laplacian -- variational methods -- weighted variable exponent Lebesgue–Sobolev spaces; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7246
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We study the existence of infinitely many solutions for a generalized p (·)‐Laplace equation involving Leray–Lions operators. Firstly, under a p (·)‐sublinear condition for nonlinear term, we obtain a sequence of solutions approaching 0 by showing a new a priori bound for solutions. Secondly, for a p (·)‐superlinear condition, we produce a sequence of solutions whose Sobolev norms diverge to infinity when the nonlinear term satisfies a couple of generalized Ambrosetti–Rabinowitz type conditions in which each associated energy functional holds the Palais–Smale condition. Lastly, we deal with a case without the Ambrosetti–Rabinowitz type condition in which an associated energy functional holds the Cerami condition and establish a sequence of solutions whose Sobolev norms diverge to infinity.