Boundary Value Problems for Second-order Integro-differential Equations in Banach Spaces

This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.

THE WELL-POSEDNESS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN COMPLEX BANACH SPACES

Let X be a complex Banach space and let B and C be two closed linear operators on X satisfying the condition D(B)?D(C),and let d∈L^(1)(R_(+))and 0≤β<α≤2.We characterize the well-posedness of the fractional integro-differential equations D^(α)u(t)+CD^(β)u(t)=Bu(t)+∫_(-∞)td(t-s)Bu(s)ds+f(t),(0≤t≤2π)on periodic Lebesgue-Bochner spaces L^(p)(T;X)and periodic Besov spaces B_(p,q)^(s)(T;X).

ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE

By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results.

PERIODIC BOUNDARY VALUE PROBLEMS FOR NONLINEAR IMPULSIVEINTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE IN BANACH SPACES

In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.

Stability for Functional Differential Equations with Delay in Banach Spaces

In this paper, using Sadovskii’s fixed point theorem and properties of the measure of noncompactness, we obtain asymptotic stability results for solutions of nonlinear differential equation with variable delay. Results presented in this paper extend some previous results due to Burton?[1], Becker and Burton?[2], Ardjouni and Djoudi [3], and Jin and Luo?[4].

Coupled Extremal Quasi-solutions to Nonlinear Impulsive Fredholm Integral Equations in Banach Spaces

By means of the method of coupled lower and upper quasisolutio ns, the paper applies, instead of establishing the comparison theorem, a new ite rative technique to nonlinear impulsive Fredholm integral equations in Banach sp aces and proves the existence theorem on their coupled extremal quasisolutions . Finally, an infinite system of nonlinear impulsive integral equations is provi ded to demonstrate the obtained results.

THE PATHWISE SOLUTION FOR A CLASS OF QUASILINEAR STOCHASTIC EQUATIONS OF EVOLUTION IN BANACH SPACE Ⅲ

This is the third part of the papers with the same title. We will discuss the problem of convergence of the semi-implicit difference scheme for a class of quasilinear SEE, which generalize the Crandall's work to the stochastic case.

Periodic Solutions of Integro-Differential Equations

The aim of this work is to study the existence of periodic solutions of integro-differential equations , (0 ≤ t ≤ 2π) with the periodic condition x(0) = x(2π) , where a ∈ L1 (R+). Our approach is based on the M-boundedness of linear operators Bsp,q-multipliers and some results in Besov space.

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated withSλand consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations.We also establish certain interesting examples to illustrate the usability of our results.

Banach空间中一类泛函方程的Ulam稳定性

结合差分算子的定义,给出二次和四次泛函方程的统一形式,使得这个新的泛函方程涵括Lee、Kayal和玉强等的结论。然后利用经典的不动点法,研究该泛函方程在Banach空间上的Ulam稳定性。最后,应用定理1.1和定理1.2所得结论,改进并推广几类已知二次和四次泛函方程的稳定性结果。

GLOBAL EXISTENCE OF SOLUTION TO NONLINEAR INTEGRODIFFERENTIAL EQUATION IN A BANACH SPACE

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.

STABILITY AND CONVERGENCE OF STEPSIZE-DEPENDENT LINEAR MULTISTEP METHODS FOR NONLINEAR DISSIPATIVE EVOLUTION EQUATIONS IN BANACH SPACE

Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach space.To break through the order barrier p≤1 of unconditionally contractive linear multistep methods for dissipative systems,strongly dissipative systems are introduced.By employing the error growth function of the methods,new contractivity and convergence results of stepsize-dependent linear multistep methods on infinite integration intervals are provided for strictly dissipative systems(ω<0)and strongly dissipative systems.Some applications of the main results to several linear multistep methods,including the trapezoidal rule,are supplied.The theoretical results are also illustrated by a set of numerical experiments.

APPROXIMATE SOLUTION OF P-RADICAL FUNCTIONAL EQUATION IN 2-BANACH SPACES

The aim of this paper is to introduce and solve the p-radical functional equation ■We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation in 2-Banach spaces.

Orthogonal Stability of Mixed Additive-Quadratic Jensen Type Functional Equation in Multi-Banach Spaces

In this paper, we prove the Hyers-Ulam stability of the following mixed additive-quadratic Jensen type functional equation:

INITIAL VALUE PROBLEMS FOR SECOND ORDER IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

This paper investigates the maximal and minimal solutions of initial value problem for second order nonlinear impulsive integro differential quation in a Banach space by establishing a comparison result and using the upper and lower solutions.

INTEGRO-DIFFERENTIAL EQUATIONS ONUNBOUNDED DOMAINS IN BANACH SPACES

This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.

Existence Solution for 5th Order Differential Equations under Some Conditions

We study a nonlinear differential equations in the Banach space of real functions and continuous on a bounded and closed interval. With the help of a suitable theorems (fixed point) and some boundary conditions, the 5th order nonlinear differential equations has at least one positive solution.

ODEs IN BANACH SPACES AND FIXED POINTS OF WEAKLY INWARD MAPS

This paper is an attempt to investigate systematically fixed points of weakly inward maps by using some basic results from differential equations in Banach spaces. By investigating the Poincare operators for such differential equations, we establish a fixed point index theory for two classes of weakly inward maps.

QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES

In this paper, we solve the quadratic p-functional inequalities ……where p is a fixed complex number with ｜P｜ 〈 1, and^where p is a fixed complex number with ｜P｜ 〈 2^-1.Using the direct method, we prove the Hyers-Ulam stability of the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces and prove the Hyers-Ulam stability of quadratic p-functional equations associated with the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces.

Iterative Solution for Systems of Nonlinear Two Binary Operator Equations

Using the cone and partial ordering theory and mixed monotone operator theory, the existence and uniqueness of solutions for some classes of systems of nonlinear two binary operator equations in a Banach space with a partial ordering are discussed. And the error estimates that the iterative sequences converge to solutions are also given. Some relevant results of solvability of two binary operator equations and systems of operator equations are improved and generalized.