The Existence of Nontrivial Solutions to a Class of Quasilinear Equations. (26th April 2021) - Jia, Xiaoyao; Lou, Zhenluo
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.