Displaying similar documents to “New existence results of anti-periodic solutions of nonlinear impulsive functional differential equations”

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.

Existence and global attractivity of positive periodic solutions for a delayed competitive system with the effect of toxic substances and impulses

Changjin Xu, Qianhong Zhang, Maoxin Liao (2013)

Applications of Mathematics

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In this paper, a class of non-autonomous delayed competitive systems with the effect of toxic substances and impulses is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantees the existence of at least one positive periodic solution, and by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are established.