The Existence of Nontrivial Solutions to a Class of Quasilinear Equations. (26th April 2021)

• Record Type: Journal Article
• Authors: Jia, Xiaoyao; Lou, Zhenluo
• Other Names: Verbitsky Igor E. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-04-26
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/9986047
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we study the following quasilinear equation: − div ϕ ∇ u ∇ u + ϕ u u = f u in ℝ N, where ϕ ∈ C 1 ℝ +, ℝ + and Φ t = ∫ 0 t s ϕ ∣ s ∣ d s . In the Orlicz-Sobolev space, by variational methods and a minimax theorem, we prove the equation has a nontrivial solution.