ON THE EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTION FOR RAYLEIGH TYPE p-LAPLACIAN EQUATION

Congmin Yang; Zhihang Xu; Zaihong Wang

Congmin Yang School of Mathematical Sciences, Capital Normal University, Beijin 100048, P. R. Chian
Zhihang Xu School of Mathematical Sciences, Capital Normal University, Beijin 100048, P. R. Chian
Zaihong Wang School of Mathematical Sciences, Capital Normal University, Beijin 100048, P. R. Chian

Article ID: 2405

Keywords: p-Laplacian equation; periodic solution; continuation theorem

Abstract

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.

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