Approximate Controllability for a Class of Abstract Second-Order Functional Evolution Equations

Results providing sufficient conditions for the approximate controllability of a class of second-order abstract functional evolution equations governed by the generator of a strongly continuous cosine family of linear operators, together with nonlocal initial conditions, are developed. This work extends results included in recent work by Naito, Park, Zhou, and others. The abstract theory is then applied to a parabolic partial integrodifferential equation.     

Controllability for Neutral Stochastic Functional Integrodifferential Infinite Delay Systems in Abstract Space

In this paper, sufficient conditions are given for the controllability of a class of neutral stochastic functional integrodifferential equations with infinite delay in abstract space. The Nussbaum fixed point theorem is adapted to obtain the controllability results, which greatly extends the previous results to the stochastic settings with the help of analytic semigroups. An example is provided to illustrate the theory.     

Local Controllability of Functional Integrodifferential Equations in Banach Space

In this paper, we establish a set of sufficient conditions for the local controllability of functional integrodifferential equations in Banach space. The results are obtained by using the methods of analytic semigroups, fractional powers of operators, and a fixed-point argument. These results generalize previous results on bounded linear operators to unbounded linear operators in which the equation involves a nonlinear delay term. An application to a partial integrodifferential equation is given.     

Projection methods for the solution of one class of singular integrodifferential equations

In this paper we propose a computational scheme of the general projection method for the solution of singular integrodifferential equations in the theory of stream lines and thermal conductivity. We theoretically substantiate this scheme from the standpoint of the theory of approximate methods of functional analysis. We consider particular cases of the general projection method, namely, the method of moments and the collocation method.     

Existence and regularity of solutions for neutral partial functional integrodifferential equations

In this paper, we study a class of neutral partial functional integrodifferential equations with finite delay by using the theory of resolvent operators. We give some sufficient conditions ensuring the existence, uniqueness and regularity of solutions. As an application, we also consider a diffusive neutral partial functional integrodifferential equation.     

Controllability of semilinear stochastic functional integrodifferential systems in Hilbert spaces

In this paper approximate and exact controllability for semilinear stochastic functional integrodifferential systems are established. The results are obtained by using the Banach fixed point theorem. An example is provided to illustrate the theory.     

Existence results for partial neutral functional integrodifferential equations with unbounded delay

We prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the Leray-Schauder alternative.     

ON SOLUTIONS TO SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper, using the theory of resolvent operators, Banach,s contraction prin-ciple and Schauder,s fixed point theorem, we study the existence of integral solutions to semilinear integrodifferential equations under nonlocal conditions in Banach space. An example is provided to illustrate the results obtained.     

Boundary and initial-value methods for solving Fredholm equations with semidegenerate kernels

We develop a new approach to the theory and numerical solution of a class of linear and nonlinear Fredholm equations. These equations, which have semidegenerate kernels, are shown to be equivalent to two-point boundary-value problems for a system of ordinary differential equations. Applications of numerical methods for this class of problems allows us to develop a new class of numerical algorithms for the original integral equation. The scope of the paper is primarily theoretical; developing the necessary Fredholm theory and giving comparisons with related methods. For convolution equations, the theory is related to that of boundary-value problems in an appropriate Hilbert space. We believe that the results here have independent interest. In the last section, our methods are extended to certain classes of integrodifferential equations.     

Controllability of Nonlinear Systems in Banach Spaces: A Survey

This paper presents a survey on research using fixed-point theorems and semigroup theory to study the controllability of nonlinear systems and functional integrodifferential systems in Banach spaces. Also discussed is the use of this technique in K-controllability and boundary controllability problems for nonlinear systems and integrodifferential systems in abstract spaces.     

Banach空间半线性积微分方程的非局部Cauchy问题

运用预解算子理论和Schauder不动点定理,在Banach空间证明了一类非局部半线性积微分方程积分解的存在性.     

Existence results for impulsive neutral evolution integrodifferential equations with infinite delay

In this paper we prove the existence of mild solutions for impulsive neutral evolution integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using the analytic semigroup theory and the Krasnoselski–Schaefer type fixed point theorem. An example is provided to illustrate the theory.     

Existence of solutions for nonlinear functional integrodifferential evolution equations with nonlocal conditions

In this paper, we prove the existence of mild solutions for nonlinear functional integrodifferential evolution equations with nonlocal conditions in Banach spaces. The results are obtained by using the theory of resolvent operators and Leray–Schauder nonlinear alternative.     

Constrained Controllability of Fractional Dynamical Systems

The article deals with the controllability results for fractional dynamical systems with prescribed controls represented by the fractional integrodifferential equation in finite dimensional spaces. Sufficient conditions for the controllability results of nonlinear fractional dynamical systems are obtained using the contraction mapping principle. Examples are included to illustrate the theory.     

Controllability of neutral functional evolution integrodifferential systems with infinite delay

In this paper we establish sufficient conditions for the controllability of neutral functional evolution integrodifferential systems. The results are obtained by using analytic semigroup theory and the Nussbaum fixed point theorem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

含多个Volterra型积分算子的积分微分方程组边值问题的奇摄动

研究含多个Volterra型积分算子的积分微分方程组Robin边值问题的奇摄动．在适当的条件下，利用微分不等式理论，证明了解的存在及解的按分量一致有效的估计．     

Study a class of Hilfer fractional stochastic integrodifferential equations with Poisson jumps

Abstract

In this article, we derive the sufficient conditions for the existence of mild solutions of Hilfer fractional stochastic integrodifferential equations with nonlocal conditions and Poisson jumps in Hilbert spaces. Results will be obtained in the pth mean square sense by using the fractional calculus, semigroup theory and stochastic analysis techniques. The article generalizes many of the existing results in the literature in terms of (1) Riemann–Liouville and Caputo derivatives are the special cases. (2) In the sense of pth mean square norm. (3) Stochastic integrodifferential with nonlocal conditions and Poisson jumps. A numerical example is provided to validate the obtained theoretical results.     

Asymptotic stability of impulsive stochastic partial integrodifferential equations with delays

In this paper, we study the existence and asymptotic stability in the p-th moment of mild solutions of nonlinear impulsive stochastic partial functional integrodifferential equations with delays. We suppose that the linear part possesses a resolvent operator in the sense given in Grimmer [R. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Am. Math. Soc. 273(1) (1982), 333–349] and the nonlinear terms are assumed to be Lipschitz continuous. A fixed point approach is employed for achieving the required result. An example is provided to illustrate the results of this work.     

Semilinear Integrodifferential Equations of Hyperbolic Type: Existence in the Large

The main object of this work is the existence of global solutions to semilinear integrodifferential equations in Hilbert spaces for absolutely continuous convolution kernels, where the nonlinear term is the gradient of a functional having superlinear growth at infinity. An application to the theory of viscoelasticity concludes the paper providing motivations for the abstract theory.     

Mild solutions of non‐Lipschitz stochastic integrodifferential evolution equations

In this work, we study the existence and uniqueness of mild solutions for stochastic partial integrodifferential equations under local non‐Lipschitz conditions on the coefficients. Our analysis makes use of the theory of resolvent operators as developed by R. Grimmer as well as a stopping time technique. Our results complement and improve several earlier related works. An example is provided to illustrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.