In this paper, we study the existence and uniqueness of periodic solution for Rayleigh type p-Laplacian equation

We prove the existence and uniqueness of periodic solution of the given equation provided that there exist constants   such that  or f is bounded below (or above) and g satisfies the monotonicity condition.

p-Laplacian equation, periodic solution, continuation theorem.

Received: February 9, 2023;  Accepted: March 18, 2023; Published: April 13, 2023

How to cite this article: Congmin Yang, Zhihang Xu and Zaihong Wang, On the existence  and uniqueness of periodic solution for Rayleigh type p-Laplacian equation, Advances in Differential Equations and Control Processes 30(2) (2023), 83-95. http://dx.doi.org/10.17654/0974324323006

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] B. Liu, Existence and uniqueness of periodic solutions for a kind of type Liénard p-Laplacian equation, Nonlinear Anal. 69 (2008), 724-729.
[2] Y. Li and L. Huang, New results of periodic solutions for forced Rayleigh-type equations, J. Comput. Appl. Math. 221 (2008), 98-105.
[3] P. Jebelean and J. Mawhin, Periodic solutions of singular nonlinear perturbations of the ordinary p-Laplacian, Advanced Nonlinear Studies 2 (2002), 299-312.
[4] M. Jiang, A Landesman-Lazer type theorem for periodic solutions of the resonant asymmetric p-Laplacian equation, Acta Math. Sin. (Engl. Ser.) 21 (2005), 1219-1228.
[5] S. Lu and Z. Gui, On the existence of periodic solutions to p-Laplacian Rayleigh differential equation with a delay, J. Math. Anal. Appl. 325 (2007), 685-702.
[6] R. Manásevich and J. Mawhin, Periodic solutions for nonlinear systems with p-Laplacian-like operators, J. Differential Equations 145 (1998), 367-393.
[7] Y. Wang, X. Dai and X. Xia, On the existence of a unique periodic solution to a Liénard type p-Laplacian non-autonomous equation, Nonlinear Anal. 71 (2009), 275-280.
[8] W. Xiong and J. Shao, Existence and uniqueness of positive periodic solutions for Rayleigh type p-Laplacian equation, Nonlinear Anal. Real World Appl. 10 (2009), 1343-1350.
[9] Y. Xin, X. Han and Z. Cheng, Existence and uniqueness of positive periodic solution for ϕ-Laplacian Liénard equation, Boundary Value Problems 2014 (2014), 244.
[10] F. Zhang and Y. Li, Existence and uniqueness of periodic solutions for a kind of Duffing type p-Laplacian equation, Nonlinear Anal. Real World Appl. 9 (2008), 985-989.