Impulsive Integro-differential Equations Research Articles

Remark on the existence results for fractional impulsive integrodifferential equations in Banach spaces

This paper deal with the study of the existence of solutions of nonlinear fractional integrodifferential equations with impulsive conditions in Banach spaces, by means of fixed point principle. The purpose of the paper is to generalize the results of [5] and correct an error in the example included in [5].

A class of BVPS for first order impulsive integro-differential equations

In this paper, we study the impulsive integro-differential equations u ′ ( t ) = f ( t , u ( t ) , Tu , Su ) , t ≠ t k , t ∈ J = [ 0 , 1 ] , Δ u ( t k ) = I k ( u ( t k ) ) , k = 1 , 2 , … , m , u ( 0 ) = au ( 1 ) + bu ( ξ ) . The existence of maximal and minimal solutions to the problem is proved by using an upper and lower solutions method together with monotone iterative technique. And two monotone sequences which uniformly converge to the relevant solutions are obtained. An example is included to show the applicability of our results.

Multiple Positive Solutions for First‐Order Impulsive Integrodifferential Equations on the Half Line in Banach Spaces

The author discusses the multiple positive solutions for an infinite boundary value problem of first‐order impulsive superlinear integrodifferential equations on the half line in a Banach space by means of the fixed point theorem of cone expansion and compression with norm type.

Correction on the paper Triple positive solutions ofn-th order impulsive integro-differential equations

Correction on the paper Triple positive solutions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>-th order impulsive integro-differential equations

Impulsive Integrodifferential Equations Involving Nonlocal Initial Conditions

We focus on a Cauchy problem for impulsive integrodifferential equations involving nonlocal initial conditions, where the linear part is a generator of a solution operator on a complex Banach space. A suitable mild solution for the Cauchy problem is introduced. The existence and uniqueness of mild solutions for the Cauchy problem, under various criterions, are proved. In the last part of the paper, we construct an example to illustrate the feasibility of our results.

Triple positive solutions of nth order impulsive integro-differential equations

Triple positive solutions of nth order impulsive integro-differential equations

Integral boundary value problems for first order impulsive integro-differential equations of mixed type

This paper considers existence of solutions for a class of first order impulsive differential equation with integral boundary value conditions. We present a new comparison theorem and show that the monotone iterative technique coupled with lower and upper solutions is still valid. The results we obtained generalize and improve many recent results.

Integral boundary value problem for impulsive integro-differential equations in Banach spaces

In this paper, by using the cone theory and monotone iterative technique, we investigate the existence of extremal solutions and unique solution of the integral boundary value problem for a class of first-order impulsive integro-differential equations in a real Banach space. An explicit iterative scheme for the unique solution and an error estimate of the approximation sequence are also derived.

Existence results for fractional impulsive integrodifferential equations in Banach spaces

This paper is mainly concerned with the existence of solutions of first order nonlinear impulsive fractional integrodifferential equations in Banach spaces. The results are obtained by using fixed point principles. Further, some interesting examples are presented to illustrate the theory.

Terminal Value Problems for Second-Order Impulsive Integro-differential Equations in Banach Space

By using the lower and upper solution method,the author studies a kind of terminal value problems for second-order impulsive integro-differential equations in a Banach space and the existence of maximal and minimal solutions are obtained.

Impulsive anti-periodic boundary value problem of first-order integro-differential equations

This paper is concerned with the anti-periodic boundary value problem of first-order nonlinear impulsive integro-differential equations. We first establish a new comparison principle, and then obtain the existence of extremal solutions by upper–lower solution and monotone iterative techniques. Some examples are presented to illustrate the main results.

Maximum principles for the periodic boundary value problem for impulsive integro-differential equations

This paper studies a first-order periodic boundary value problem for impulsive integro-differential equations and establishes some new maximum principles. Some points of a recent paper are also corrected and extended.

The Existence and Exponential Stability for Random Impulsive Integrodifferential Equations of Neutral Type

The Existence and Exponential Stability for Random Impulsive Integrodifferential Equations of Neutral Type

Multiple positive solutions for second order impulsive boundary value problems in Banach spaces

By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral bound- ary conditions in a Banach space. Moreover, an application is given to illustrate the

The Existence and Exponential Stability for Random Impulsive Integrodifferential Equations of Neutral Type

By applying the Banach fixed point theorem and using an inequality technique, we investigate a kind of random impulsive integrodifferential equations of neutral type. Some sufficient conditions, which can guarantee the existence, uniqueness, and exponential stability in mean square for such systems, are obtained. Compared with the previous works, our method is new and our results can generalize and improve some existing ones. Finally, an illustrative example is given to show the effectiveness of the proposed results.

Necessary conditions of optimality for second-order nonlinear impulsive integro-differential equations on Banach spaces

We discuss a class of optimal control problems of systems governed by the second-order nonlinear impulsive integro-differential equations with time-varying generating operators in fractional power spaces. Introducing the reasonable P C – α -mild solution of the second-order nonlinear impulsive integro-differential equations we prove the existence of P C – α -mild solutions. Existence of optimal controls for a Lagrange problem of systems governed by the second-order nonlinear impulsive integro-equations is presented. We apply a direct approach to derive the maximum principle for the problem at hand.

Existence of solutions of boundary value problems with integral boundary conditions for second-order impulsive integro-differential equations in Banach spaces

This paper investigates the existence of solutions for a class of second-order boundary-value problems with integral boundary conditions of nonlinear impulsive integro-differential equations in Banach spaces. The arguments are based upon the fixed point theorem of strict set contraction operators. Meanwhile, an example is worked out to demonstrate the main results.

A class of nonlinear integrodifferential impulsive periodic systems of mixed type and optimal controls on Banach space

A class of nonlinear integrodifferential impulsive periodic systems of mixed type on Banach space is considered. Existence of periodic PC-mild solutions is proved. Existence of periodic optimal pairs of systems governed by nonlinear impulsive integrodifferential equations of mixed type is also presented. An example is given for demonstration.

Approximate controllability of nonlinear stochastic impulsive integrodifferential systems in hilbert spaces

Many practical systems in physical and biological sciences have impulsive dynamical behaviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability properties of nonlinear stochastic impulsive integrodifferential and neutral functional stochastic impulsive integrodifferential equations in Hilbert spaces. Assuming the conditions for the approximate controllability of these linear systems we obtain the sufficient conditions for the approximate controllability of these associated nonlinear stochastic impulsive integrodifferential systems in Hilbert spaces. The results are obtained by using the Nussbaum fixed-point theorem. Finally, two examples are presented to illustrate the utility of the proposed result.

New results for the second order impulsive integro-differential equations with nonlinear boundary conditions

This paper considers the second order integro-differential equations with impulses. Some sufficient conditions for the existence of solutions are proposed by using monotone iterative method and Schauder fixed point theorem. Moreover, new concepts of lower and upper solutions are introduced for nonlinear boundary value problems.