Abstract

ON THE EXISTENCE AND UNIQUENESS OF 2?-PERIODIC SOLUTIONS OF DUFFING?S EQUATION USING ABSTRACT IMPLICIT FUNCTION THEOREM IN BANACH SPACES

E.O. Eze and C.O.D. Udaya

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We applied the conditions of Implicit function theorem to investigate the existence and uniqueness of 2?-periodic solution of Duffing?s equation of the form x ?-(cx) ?-bx-?2x?^3=h(t) The solutions were found to exist and are unique under some appropriate assumptions because many systems are periodic in nature, yet they do not obey periodic solutions. Keywords: Implicit function theorem, Duffing?s equation, Periodic solutions, Banach spaces, Homeomorphism.

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