Displaying similar documents to “On the Kneser-type solutions for two-dimensional linear differential systems with deviating arguments.”

New existence results of anti-periodic solutions of nonlinear impulsive functional differential equations

Yuji Liu, Xingyuan Liu (2013)

Mathematica Bohemica

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This paper is a continuation of Y. Liu, Anti-periodic solutions of nonlinear first order impulsive functional differential equations, Math. Slovaca 62 (2012), 695–720. By using Schaefer's fixed point theorem, new existence results on anti-periodic solutions of a class of nonlinear impulsive functional differential equations are established. The techniques to get the priori estimates of the possible solutions of the mentioned equations are different from those used in known papers. An...

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.