Open AccessThe Existence of Nontrivial Solutions to a Class of Quasilinear Equations
Author(s) -
Xiaoyao Jia,
Zhenluo Lou
Publication year - 2021
Publication title -
journal of function spaces
Language(s) - English
Resource type - Journals
eISSN - 2314-8896
pISSN - 2314-8888
DOI - 10.1155/2021/9986047
Subject(s) - class (philosophy) , mathematics , pure mathematics , mathematical economics , mathematical analysis , computer science , artificial intelligence
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.
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