Order Impulsive Integro-differential Equations Research Articles

Holder's Inequality ρ–Mean Continuity for Existence and Uniqueness Solution of Fractional Multi-Integrodifferential Delay System

We herein present the detailed results for the existence and uniqueness of mild solution for multifractional order impulsive integrodifferential control equations with a nonlocal condition involving several types of semigroups of bounded linear operators, which were established on probability density functions related with the fractional differential equation. Additionally, we present the necessary and sufficient conditions to investigate Schauder’s fixed point theorem with Holder’s inequality ρ–mean continuity and infinite delay parameter to guarantee the uniqueness of a fixed point.

Existence of two positive solutions for a class of second order impulsive singular integro-differential equations on the half line

In this paper, the author discusses the existence of two positive solutions for an infinite boundary value problem of second order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.

Multi-point boundary value problem for first order impulsive integro-differential equations with multi-point jump conditions

In this article we introduce a new definition of impulsive conditions for boundary value problems of first order impulsive integro-differential equations with multi-point boundary conditions. By using the method of lower and upper solutions in reversed order coupled with the monotone iterative technique, we obtain the extremal solutions of the boundary value problem. An example is also discussed to illustrate our results. Mathematics Subject Classification 2010: 34B15; 34B37.

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.

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

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.

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.

A class of second order impulsive integro-differential equations on unbounded domain in a Banach space

In this paper, by using the cone theory and monotone iterative technique, we investigate the existence of extremal solutions and unique solution of the initial value problem (IVP) for a class of second order impulsive integro-differential equations on unbounded domain in a Banach space. Our results improve and extend many recent results.

Nonlinear boundary value problem for second order impulsive integro-differential equations of mixed type in Banach space

Using the cone theory and lower and upper solutions, we investigate the existence of extremal solutions of nonlinear boundary value problem for second order impulsive integro-differential equations, which involve the derivative x ′ and deviating argument x ( β ( t ) ) in Banach space.

New existence theorem for impulsive integro-differential equations of mixed type

In this paper, we investigate the nonlinear boundary value problem for first order impulsive integro-differential equations of mixed type. New existence theorem of extremal solutions is established by new comparison principles and the monotone iterative technique. The result improves and extends the known relevant conclusion in the literature. Example is also provided to illustrate the advantage of our result.

Existence of solutions of nth order impulsive integro-differential equations in Banach spaces

In this paper, we prove the existence of solutions of initial value problems for nth order nonlinear impulsive integro-differential equations of mixed type on an infinite interval with an infinite number of impulsive times in Banach spaces. Our results are obtained by introducing a suitable measure of noncompactness.

Initial value problems for first order impulsive integro-differential equations of Volterra type in Banach spaces

In this paper, we use a new method and combining the partial ordering method to study the existence of the solutions for the first order nonlinear impulsive integro-differential equations of Volterra type on finite interval in Banach spaces and for the first order nonlinear impulsive integro-differential equations of Volterra type on infinite interval with infinite number impulsive times in Banach spaces. By introducing an interim space and using progressive estimation method, some restrictive conditions on impulsive terms, used before, such as, prior estimation, noncompactness measure estimations are deleted.

Global solutions of nonlinear second-order impulsive integro-differential equations of mixed type in Banach spaces

In this paper, by using the generalization of Darbo’s fixed point theorem, we establish the existence of global solutions of an initial value problem for a class of second-order impulsive integro-differential equations of mixed type in a real Banach space. Our results generalize and improve on the results of Guo et al. [F. Guo, L.S. Liu, Y.H. Wu, P. Siew, Global solutions of initial value problems for nonlinear second-order impulsive integro-differential equations of mixed type in Banach spaces, Nonlinear Anal. 61 (2005) 1363–1382] in the sense that the conditions for existence of global solution in our theorem is simpler and less strict. To demonstrate the application of the theorem, we give the global solutions of two mixed boundary value problems for two classes of fourth order impulsive integro-differential equations.

Nonlinear boundary problem of first order impulsive integro-differential equations

This paper focuses on first-order impulsive integro-differential equations with nonlinear boundary. The lower and upper solutions combined with monotone iterative techniques are used to obtain the existence of extremal solutions of the problem. Numerical examples are given to prove its validity.

Nonlinear boundary value problem for first order impulsive integro-differential equations of mixed type

This paper discusses nonlinear boundary value problem for first order impulsive integro-differential equations of mixed type. The lower and upper solutions and monotone iterative techniques are used to achieve the existence results. Two examples are provided to illustrate the efficiency of the obtained results.

Initial value problems for nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces

In this paper, through solving equations step by step, without any assumption of compactness-type conditions, we obtain unique solution of initial value problems of nonlinear second order impulsive integral-differential in Banach spaces. The results obtained generalize and improve the corresponding results of Guo and Chai in papers [D.J. Guo, Initial value problems for nonlinear second-order impulsive integro-differential equations in Banach spaces, J. Math. Anal. Appl. 200 (1996) 1–13; G.Q. Chai, Initial value problems for nonlinear second order impulsive integro-differential equations in Banach space, Acta Math. Sinica 20 (3) (2000) 351–359 (in Chinese)].

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

This paper investigates the existence of minimal and maximal solutions of periodic boundary value problem for first order impulsive integro-differential equations of mixed type by establishing a comparison result and using the method of upper and lower solutions and the monotone iterative technique.

A class of nth-order impulsive integrodifferential equations in Banach spaces

By establishing a comparison result and using the monotone iterative technique, the author obtains the existence of maximal and minimal solutions of the initial value problem for a class of n th -order impulsive integrodifferential equations in a Banach space.

A unique solution of initial value problems for first order impulsive integro-differential equations of mixed type in Banach spaces

In this paper, we investigate initial value problem for first order impulsive integro-differential equation of mixed type in a Banach space. Without any compactness-type assumption, we obtain a unique solution of the equation, an explicit iterative approximation of the solution and an error estimate of the approximation sequence. Our result improves and extends many recent results.