Existence of Periodic Solutions for Second-Order Ordinary p -Laplacian Systems

Shaomin Wang (), Cunji Yang and Guozhi Cha
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Shaomin Wang: School of Mathematics and Computer, Dali University, Dali 671003, China
Cunji Yang: School of Mathematics and Computer, Dali University, Dali 671003, China
Guozhi Cha: School of Engineering, Dali University, Dali 671003, China

Mathematics, 2024, vol. 12, issue 8, 1-12

Abstract: In this paper, we study the variational principle and the existence of periodic solutions for a new class of second-order ordinary p -Laplacian systems. The variational principle is given by making use of two methods. We obtain three existence theorems of periodic solutions to this problem on various sufficient conditions on the potential function F ( t , x ) or nonlinearity ∇ F ( t , x ) . Four examples are presented to illustrate the feasibility and effectiveness of our results.

Keywords: ordinary p -Laplacian system; the variational principle; periodic solutions; the least action principle; saddle point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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