增算子不动点定理及其对含间断项非线性脉冲方程的应用

设E是Banach空间,本文在比C[I,E]更一般的Banach空间中得到了几个新的非连续增算子不动点定理.作为应用,我们研究了Banach空间中含间断项的非线性脉冲积分方程和微分方程的最大解和最小解的存在性.     

Local and global existence of mild solutions for impulsive fractional semilinear integro-differential equation

In this paper, we study the local and global existence of mild solutions for impulsive fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space. Also, we review some applications of fractional differential equations.     

The uniqueness of a solution to the inverse Cauchy problem for a fractional differential equation in a Banach space

We consider linear fractional differential operator equations involving the Caputo derivative. The goal of this paper is to establish conditions for the unique solvability of the inverse Cauchy problem for these equations. We use properties of the Mittag-Leffler function and the calculus of sectorial operators in a Banach space. For equations with operators in a general form we obtain sufficient conditions for the unique solvability, and for equations with densely defined sectorial operators we obtain necessary and sufficient unique solvability conditions.     

Semilinear fractional integro-differential equations with compact semigroup

In this paper, we study the local and global existence of mild solutions to a class of fractional integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space.     

Semilinear fractional integro-differential equations with compact semigroup

In this paper, we study the local and global existence of mild solutions to a class of fractional integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space.     

Evolution Systems for Differential Equations with Variable Time Lags

We consider nonautonomous retarded functional differential equations under hypotheses which are designed for the application to equations with variable time lags, which may be unbounded, and construct an evolution system of solution operators which are continuously differentiable. These operators are defined on manifolds of continuously differentiable functions. The results apply to pantograph equations and to nonlinear Volterra integro-differential equations, for example. For linear equations we also provide a simpler evolution system with solution operators on a Banach space of continuous functions.     

Degenerate integro-differential operators in Banach spaces and their applications

In this paper we consider linear integro-differential equations in Banach spaces with Fredholm operators at the highest-order derivatives and convolution-type Volterra integral parts. We obtain sufficient conditions for the unique solvability (in the classical sense) of the Cauchy problem for the mentioned equations and illustrate the abstract results with pithy examples. The studies are carried out in classes of distributions in Banach spaces with the help of the theory of fundamental operator functions of degenerate integro-differential operators. We propose a universal technique for proving theorems on the form of fundamental operator functions.     

Random fixed point theorems for Hardy-Rogers self-random operators with applications to random integral equations

In this paper, we prove some random fixed point theorems for Hardy–Rogers self-random operators in separable Banach spaces and, as some applications, we show the existence of a solution for random nonlinear integral equations in Banach spaces. Some stochastic versions of deterministic fixed point theorems for Hardy–Rogers self mappings and stochastic integral equations are obtained.     

Nonlinear random equations involving completely closed operators

We introduce the concept of completely closed operators in Banach spaces and then obtain the existence of random solutions of operator equations involving such operators. As simple corollaries we obtain the existence theorems for random operator equations involving monotone operators as well as operators of type (M).     

Solvability criterion and representation of solutions of <Emphasis Type="Italic">n</Emphasis>-normal and <Emphasis Type="Italic">d</Emphasis>-normal linear operator equations in a Banach space

On the basis of a generalization of the well-known Schmidt lemma to the case of n-normal and d-normal linear bounded operators in a Banach space, we propose constructions of generalized inverse operators. We obtain criteria for the solvability of linear equations with these operators and formulas for the representation of solutions of these equations.     

Unbounded perturbation of the controllability for evolution equations

In this paper we prove that the controllability for evolution equations in Banach spaces is not destroyed, if we perturb the equation by “small” unbounded linear operator. This is done by employing a perturbation principle from linear operator theory and a characterization of surjective operators in Banach spaces. Finally, we apply these to a control system governed by partial integro-differential equations.     

Factoring weakly compact operators and the inhomogeneous Cauchy problem

By using the technique of factoring weakly compact operators through reflexive Banach spaces we prove that a class of ordinary differential equations with Lipschitz continuous perturbations has a strong solution when the problem is governed by a closed linear operator generating a strongly continuous semigroup of compact operators.

     

Local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces

In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense of Grimmer [R. Grimmer, Resolvent operators for integral equations in a Banach space, Transactions of the American Mathematical Society 273 (1982) 333–349]. The delayed part is assumed to be locally Lipschitz. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of strict solutions.     

New fixed point theorems in Banach algebras under weak topology features and applications to nonlinear integral equations

We introduce a class of Banach algebras satisfying certain sequential condition (P) and we prove fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operators. Later on, we give some examples of applications of these types of results to the existence of solutions of nonlinear integral equations in Banach algebras.     

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.     

一个非连续增算子不动点定理及其应用

本文在无限区间上给出了一个新的非连续增算子不动点定理。作为应用,我们研究了无限区间上Banach空间中非线性积－微分方程初值问题解的存在性。     

Existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces

In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense given by Grimmer in [R. Grimmer, Resolvent operators for integral equations in a Banach space, Transaction of American Mathematical Society 273 (1982) 333–349]. The delayed part is assumed to be locally Lipschitz. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of the strict solutions.     

Measure of noncompactness and semilinear nonlocal functional differential equations in Banach spaces

This paper is concerned with the measure of noncompactness in the spaces of continuous functions and semilinear functional differential equations with nonlocal conditions in Banach spaces.The relationship between the Hausdorff measure of noncompactness of intersections and the modulus of equicontinuity is studied for some subsets related to the semigroup of linear operators in Banach spaces.The existence of mild solutions is obtained for a class of nonlocal semilinear functional differential equations without the assumption of compactness or equicontinuity on the associated semigroups of linear operators.     

Elements of the Theory of Linear Volterra Operators in Banach Spaces

The new definition of Volterra operator introduced in [5] allows specification of the classical theory of linear equations in Banach spaces to equations with such operators. Here we specially address relations between properties of the given linear equation with Volterra operator and properties of its conjugate. As well we treat the theory of Noetherian and Fredholm equations.     

Fredholm Operators, Essential Spectra and Application to Transport Equations

In this paper the essential spectra of closed, densely defined linear operators is characterized on a Banach spaces under perturbations of n-strictly power compact operators. Further we apply the obtained results to investigate the essential spectra of one-dimensional transport equation with general boundary conditions and the essential spectra of singular neutron transport equations in bounded geometries.