Existence and multiplicity solutions for discrete Kirchhoff type problems. (April 2022)

• Record Type: Journal Article
• Authors: Long, Yuhua; Deng, Xiaoqing
• Is Part Of: Applied mathematics letters. Volume 126(2022)
• Publication Date: 2022-04
• Subjects: Discrete Kirchhoff type problem -- Sign-changing solution -- Multiple solution -- Mountain pass theorem -- Invariant sets of descending flow; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107817
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we make use of minimax methods and invariant sets of descending flow to study superlinear discrete Kirchhoff type problems. We give two interesting results: one concerns the existence of a nontrivial solution and the other deals with multiple solutions which are composed of sign-changing solution, positive solution and negative solution.