This article concerns the construction of approximate solutions for a general stochastic integrodifferential equation which is not explicitly solvable and whose coeffcients functionally depend on Lebesgue integrals an...This article concerns the construction of approximate solutions for a general stochastic integrodifferential equation which is not explicitly solvable and whose coeffcients functionally depend on Lebesgue integrals and stochastic integrals with respect to martingales. The approximate equations are linear ordinary stochastic differential equations, the solutions of which are defined on sub-intervals of an arbitrary partition of the time interval and connected at successive division points. The closeness of the initial and approximate solutions is measured in the L^p-th norm, uniformly on the time interval. The convergence with probability one is also given.展开更多
Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an e...Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.展开更多
In this Paper. by using the pseudo-spectral method of Fornberg and Whitham, a nonlinear integrodifferential equations is investigated numerically. It is found that for small ∈, the result is close to that of the KdV ...In this Paper. by using the pseudo-spectral method of Fornberg and Whitham, a nonlinear integrodifferential equations is investigated numerically. It is found that for small ∈, the result is close to that of the KdV equation, whereas the effects of larger ∈ and the initial condition are significant.展开更多
In this paper we prove the existence of mild solutions of a general class of nonlinear evolution integrodifferential equation in Banach spaces. Based on the resolvent operator and the Schaefer fixed point theorem, a s...In this paper we prove the existence of mild solutions of a general class of nonlinear evolution integrodifferential equation in Banach spaces. Based on the resolvent operator and the Schaefer fixed point theorem, a sufficient condition for the existence of general integrodifferential evolution equations is established.展开更多
A fixed point analysis approach is used to investigate the existence of mild solutions of second order semilinear impulsive delay integrodifferential equations with nonlocal conditions.Without imposing compactness con...A fixed point analysis approach is used to investigate the existence of mild solutions of second order semilinear impulsive delay integrodifferential equations with nonlocal conditions.Without imposing compactness condition on the cosine family of operators,we give some sufficient conditions for the existence of mild solutions of such system.Finally,an example is presented to illustrate the utility of the proposed result.The results improve some recent results.展开更多
In this paper, we establish sufficient conditions for existence and controllability of nonlinear neutral evolution integroditferential systems in Banach spaces. The result is obtained by using the resolvent operators ...In this paper, we establish sufficient conditions for existence and controllability of nonlinear neutral evolution integroditferential systems in Banach spaces. The result is obtained by using the resolvent operators and fixed point analysis approach.展开更多
Based on the discussion of the semidiscretization of a parabolic equation with asemilinear memory term,an error estimate is derived for the fully discrete scheme with spectral method in space and the backward Euler me...Based on the discussion of the semidiscretization of a parabolic equation with asemilinear memory term,an error estimate is derived for the fully discrete scheme with spectral method in space and the backward Euler method in time The trapezoidal rule is adopted.for the quadrature of the memory term and the quadrature error isestimated.展开更多
In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hi...In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional derivative.First,we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus,successive approximation method and stochastic analysis techniques.Second,the optimal control of the proposed problem is presented by using Balder’s theorem.Finally,an example is demonstrated to illustrate the obtained theoretical results.展开更多
In this paper, we study operators generated by Volterra-Stieltjes integrodifferential expressions. The selfadjoint boundary conditions are obtained in both regular and limit circle cases. The complete description...In this paper, we study operators generated by Volterra-Stieltjes integrodifferential expressions. The selfadjoint boundary conditions are obtained in both regular and limit circle cases. The complete description of selfadjoint extensions are given.展开更多
We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ ...We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.展开更多
In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions usin...In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions using Hausdorff measure of noncompactness, Sadovskii fixed point theorem and operator semigroups in particular dropping compactness of the operator.展开更多
In this paper we study the higher accuracy methods-the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of hyperbolicintegrodifferential equations. The global extrapola...In this paper we study the higher accuracy methods-the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of hyperbolicintegrodifferential equations. The global extrapolation and the correction approximationsof third order, rather than the pointwise extrapolation results, are derived.展开更多
This paper deals with the uniqueness and existence of periodic solutions of neutral Volterraintegrodifferential equations (1) and (2). Some new unique existence criteria are obtained.
We study the approximate controllability of control systems governed by a class of semilinear integrod- ifferential equations with infinite delays. Sufficient conditions for approximate controllability of semilinear c...We study the approximate controllability of control systems governed by a class of semilinear integrod- ifferential equations with infinite delays. Sufficient conditions for approximate controllability of semilinear control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using fixed-point theorems and semigroup theory. As an illustration of the application of the approximate controllability results, a simple example is provided.展开更多
In this paper, we discuss the maximum and minimum solutions as will as generalized maximum and minimum solutions of nonlinear integrodifferential equations of mixed type with impulses at fixed moments in Banach soaces...In this paper, we discuss the maximum and minimum solutions as will as generalized maximum and minimum solutions of nonlinear integrodifferential equations of mixed type with impulses at fixed moments in Banach soaces by the theorems of fixed points for inreasing operators.展开更多
In this paper we give the existence and uniqueness of solutions for boundary value problems of the form u' = f(t, u,u', T1u,T2u), g(u(0),u(1)) = 0, h(w(0), u(1),u'(0), u'(1)) = 0 by means of the upper ...In this paper we give the existence and uniqueness of solutions for boundary value problems of the form u' = f(t, u,u', T1u,T2u), g(u(0),u(1)) = 0, h(w(0), u(1),u'(0), u'(1)) = 0 by means of the upper and lower solution method.展开更多
In this paper, we study the controllability results for the nonlinear impulsive integrodifferential evolution systems with time-varying delays in Banach spaces. The sufficient conditions of exact controllability is pr...In this paper, we study the controllability results for the nonlinear impulsive integrodifferential evolution systems with time-varying delays in Banach spaces. The sufficient conditions of exact controllability is proved under without assuming the compactness of the evolution operator. The results are obtained by using the semigroup theory and the Schafer fixed point theorem.展开更多
In this paper,we study the complete controllability for a class of nonlinear neutral fractional integro-differential systems in a finite interval of time by means of controls whose initial and final values can be assi...In this paper,we study the complete controllability for a class of nonlinear neutral fractional integro-differential systems in a finite interval of time by means of controls whose initial and final values can be assigned in advance.The result is achieved using the Banach fixedpoint theorem and Schauder’s fixed-point theorem.Some numerical examples are provided to demonstrate the effectiveness of the main result.展开更多
In this paper Wintner type global existence results for certain higher order integrodifferential equations are established. Our analysis is based on a simple and classical application of the Leray--Schauder alternative.
文摘This article concerns the construction of approximate solutions for a general stochastic integrodifferential equation which is not explicitly solvable and whose coeffcients functionally depend on Lebesgue integrals and stochastic integrals with respect to martingales. The approximate equations are linear ordinary stochastic differential equations, the solutions of which are defined on sub-intervals of an arbitrary partition of the time interval and connected at successive division points. The closeness of the initial and approximate solutions is measured in the L^p-th norm, uniformly on the time interval. The convergence with probability one is also given.
文摘Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.
文摘In this Paper. by using the pseudo-spectral method of Fornberg and Whitham, a nonlinear integrodifferential equations is investigated numerically. It is found that for small ∈, the result is close to that of the KdV equation, whereas the effects of larger ∈ and the initial condition are significant.
文摘In this paper we prove the existence of mild solutions of a general class of nonlinear evolution integrodifferential equation in Banach spaces. Based on the resolvent operator and the Schaefer fixed point theorem, a sufficient condition for the existence of general integrodifferential evolution equations is established.
基金National Natural Science Foundation of China(No.10971139)
文摘A fixed point analysis approach is used to investigate the existence of mild solutions of second order semilinear impulsive delay integrodifferential equations with nonlocal conditions.Without imposing compactness condition on the cosine family of operators,we give some sufficient conditions for the existence of mild solutions of such system.Finally,an example is presented to illustrate the utility of the proposed result.The results improve some recent results.
文摘In this paper, we establish sufficient conditions for existence and controllability of nonlinear neutral evolution integroditferential systems in Banach spaces. The result is obtained by using the resolvent operators and fixed point analysis approach.
文摘Based on the discussion of the semidiscretization of a parabolic equation with asemilinear memory term,an error estimate is derived for the fully discrete scheme with spectral method in space and the backward Euler method in time The trapezoidal rule is adopted.for the quadrature of the memory term and the quadrature error isestimated.
文摘In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional derivative.First,we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus,successive approximation method and stochastic analysis techniques.Second,the optimal control of the proposed problem is presented by using Balder’s theorem.Finally,an example is demonstrated to illustrate the obtained theoretical results.
文摘In this paper, we study operators generated by Volterra-Stieltjes integrodifferential expressions. The selfadjoint boundary conditions are obtained in both regular and limit circle cases. The complete description of selfadjoint extensions are given.
基金Project supported by the National Natural Science Foundation of China
文摘We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.
基金supported by University Grant Commission (UGC), India (No. G2/1287/UGC SAP DRS/2009)
文摘In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions using Hausdorff measure of noncompactness, Sadovskii fixed point theorem and operator semigroups in particular dropping compactness of the operator.
文摘In this paper we study the higher accuracy methods-the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of hyperbolicintegrodifferential equations. The global extrapolation and the correction approximationsof third order, rather than the pointwise extrapolation results, are derived.
基金project is supported by National Natural Science Foundation of China
文摘This paper deals with the uniqueness and existence of periodic solutions of neutral Volterraintegrodifferential equations (1) and (2). Some new unique existence criteria are obtained.
文摘We study the approximate controllability of control systems governed by a class of semilinear integrod- ifferential equations with infinite delays. Sufficient conditions for approximate controllability of semilinear control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using fixed-point theorems and semigroup theory. As an illustration of the application of the approximate controllability results, a simple example is provided.
文摘In this paper, we discuss the maximum and minimum solutions as will as generalized maximum and minimum solutions of nonlinear integrodifferential equations of mixed type with impulses at fixed moments in Banach soaces by the theorems of fixed points for inreasing operators.
文摘In this paper we give the existence and uniqueness of solutions for boundary value problems of the form u' = f(t, u,u', T1u,T2u), g(u(0),u(1)) = 0, h(w(0), u(1),u'(0), u'(1)) = 0 by means of the upper and lower solution method.
文摘In this paper, we study the controllability results for the nonlinear impulsive integrodifferential evolution systems with time-varying delays in Banach spaces. The sufficient conditions of exact controllability is proved under without assuming the compactness of the evolution operator. The results are obtained by using the semigroup theory and the Schafer fixed point theorem.
基金UGC New Delhi for providing BSR fellowship.Notes on。
文摘In this paper,we study the complete controllability for a class of nonlinear neutral fractional integro-differential systems in a finite interval of time by means of controls whose initial and final values can be assigned in advance.The result is achieved using the Banach fixedpoint theorem and Schauder’s fixed-point theorem.Some numerical examples are provided to demonstrate the effectiveness of the main result.
文摘In this paper Wintner type global existence results for certain higher order integrodifferential equations are established. Our analysis is based on a simple and classical application of the Leray--Schauder alternative.
