Displaying similar documents to “Sufficient conditions for oscillations of all solutions of a class of impulsive differential equations with deviating argument.”

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

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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.