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Displaying similar documents to “Existence of solutions of periodic boundary value problems for impulsive functional Duffing equations at nonresonance case.”

A survey and some new results on the existence of solutions of IPBVPs for first order functional differential equations

Yuji Liu (2009)

Applications of Mathematics

Similarity:

This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation x ' ( t ) = f ( t , x ( t ) , x ( α 1 ( t ) ) , , x ( α n ( t ) ) ) for a.e. t [ 0 , T ] , Δ x ( t k ) = I k ( x ( t k ) ) , k = 1 , , m , x ( 0 ) = x ( T ) . We first present a survey and then obtain new sufficient conditions for the existence of at least one solution by using Mawhin’s continuation theorem. Examples are presented to illustrate the main results.