ON THE EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTION FOR RAYLEIGH TYPE p-LAPLACIAN EQUATION
Keywords:
p-Laplacian equation, periodic solution, continuation theoremDOI:
https://doi.org/10.17654/0974324323006Abstract
In this paper, we study the existence and uniqueness of periodic solution for Rayleigh type $p$-Laplacian equation $$\left(\phi_p\left(x^{\prime}(t)\right)\right)^{\prime}+f\left(t, x^{\prime}(t)\right)+g(t, x(t))=e(t)$$We prove the existence and uniqueness of periodic solution of the given equation provided that there exist constants $a>0, b>0$ such that $$|f(t, s)| \leq a|s|^{p-1}+b, \forall(t, s) \in \mathbb{R}^2$$ or $f$ is bounded below (or above) and $g$ satisfies the monotonicity condition.
Received: February 9, 2023
Accepted: March 18, 2023
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