Displaying similar documents to “Existence of solutions for second-order nonlinear impulsive differential equations with periodic boundary value conditions.”

On the existence of solutions for nonlinear impulsive periodic viable problems

Tiziana Cardinali, Raffaella Servadei (2004)

Open Mathematics

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In this paper we prove the existence of periodic solutions for nonlinear impulsive viable problems monitored by differential inclusions of the type x′(t)∈F(t,x(t))+G(t,x(t)). Our existence theorems extend, in a broad sense, some propositions proved in [10] and improve a result due to Hristova-Bainov in [13].

Second order nonlinear differential equations with linear impulse and periodic boundary conditions

Aydin Huseynov (2011)

Applications of Mathematics

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In this study, we establish existence and uniqueness theorems for solutions of second order nonlinear differential equations on a finite interval subject to linear impulse conditions and periodic boundary conditions. The results obtained yield periodic solutions of the corresponding periodic impulsive nonlinear differential equation on the whole real axis.

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.