Demidovic’s Limiting Regime To A Certain Fourth Order Nonlinear Differential Equation: Another Result

Abstract

In this paper, we use the Lyapunov’s second method to solve an age long problem on limiting regime in the sense of Demidovic for a general fourth order nonlinear differential equation. Sufficient conditions for the existence of a unique solution to be a limiting regime, periodic (or almost periodic) according as the forcing term is periodic (or almost periodic) are established for the concerned equation. Our results improve and generalize earlier ideas of Afuwape [A.U. Afuwape, On the existence of a limiting regime in the sense of Demidovic for a certain fourth order nonlinear differential equation, JMAA, 129, (1988) 389-393].