Integral Equations In Banach Spaces Research Articles

On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock–Kurzweil integrals

We prove some existence theorems for nonlinear integral equations of the Urysohn type $x(t)=\varphi (t)+\lambda \int _0^a f(t,s,x(s))\, ds$ and Volterra type $x(t)=\varphi (t)+\int _0^tf(t,s,x(s))\, ds$, $t\in I_a=[0,a]$, where $f$ and $\varphi $ are func

Global solutions of systems of nonlinear impulsive Volterra integral equations in banach spaces

The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence theorems of extremal solutions are obtained, which extend the related results for this class of equations on a finite interval with a finite number of moments of impulse effect. The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.

Existence criteria for integral equations in banach spaces

Existence criteria for integral equations in banach spaces

Existence theorems of solutions for nonlinear impulsive Volterra integral equations in Banach spaces

In this paper, the Monch fixed point theorem and an impulsive integral inequality is used to prove some existence theorems of solutions for nonlinear impulsive Volterra integral equations in Banach spaces that improve and extend the previous results.

Existence of solutions for nonlinear impulsive Hammerstein integral equations in Banach spaces

The existence of solutions for nonlinear impulsive Hammerstein integral equations with infinite numbers of moments of impulse effect on the infinite intervalR + in Banach spaces is studied. By means of Monch fixed point theorem, an existence theorem of solutions is obtained. The result is demonstrated by means of an infinite system for impulsive integral equations.

EIGENVECTORS OF SYSTEM OF HAMMERSTEIN INTEGRAL EQUATIONS IN BANACH SPACES AND APPLICATIONS

In this paper, the author investigates the existence of eigenvectors of system of Hammerstein integral equations in Banach spaces by means of fixed point index theory. He also gives some applications to a system of Sturm-Liouville problems of ordinary differential equations.

Existence theorems of solutions for nonlinear impulsive volterra integral equations in banach spaces

In this paper, we use the Monch fixed-point theorem to prove some existence theorems of solutions for the nonlinear impulsive Volterra integral equations in Banach spaces that improve and extend the results in [2].

Volterra and Urysohn integral equations in Banach spaces

We use topological methods to present existence principles and theory for integral equations in Banach spaces.

ON Llocp-SOLUTIONS OF NONLINEAR IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES

In this paper, we give some results on the existence of Llocp-solutions of nonlinear impulsive Volterra integral equations in Banach spaces and on the structure of the set of Llocp-solutions by the theory of Fréchet spaces.

A fixed point theorem for condensing operators and applications to Hammerstein integral equations in Banach spaces

We prove a fixed point theorem of Furi Pera type for condensing operators. This will then be used to establish the existence of solutions to certain integral equations of Hammerstein type in Banach spaces.

Existence of solutions of fuzzy integral equations in Banach spaces

We prove existence theorems for solutions of fuzzy integral equations.

Weak and strong topologies and integral equations in Banach spaces

The Schauder–Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel’skĭi’s fixed point theorem due to Nashed and Wong are used to establish existence of L and C solutions to Volterra and Hammerstein integral equations in Banach spaces.

Linearized stability for semilinear Volterra integral equations

We give a principle of linearized stability of stationary solutions of semilinear Volterra integral equations in Banach spaces.

Nonlinear impulsive Volterra integral equations in Banach spaces and applications

In this paper, we first extend results on the existence of maximal solutions for nonlinear Volterra integral equations in Banach spaces to impulsive Volterra integral equations. Then, we give some applications to initial value problems for first order impulsive differential equations in Banach spaces. The results are demonstrated by means of an example of an infinite system for impulsive differential equations.

Impulsive integral equations in Banach spaces and applications

In this paper, we first use the fixed point theory to prove two existence theorems of positive solutions for the impulsive Fredholm integral Equations in Banach spaces. And then, we offer some applications to the two‐point boundary value problems for the second order impulsive differential equations in Banach spaces.

On the structure of $L_{φ}$-solution sets of integral equations in Banach spaces

On the structure of $L_{φ}$-solution sets of integral equations in Banach spaces

Generic properties of infinite system of integral equations in Banach spaces

Generic properties of infinite system of integral equations in Banach spaces

On infinite systems of Volterra integral equations in Banach spaces

On infinite systems of Volterra integral equations in Banach spaces

The Generic Property of Existence of Solutions of Integral Equations in Banach Spaces

The Generic Property of Existence of Solutions of Integral Equations in Banach Spaces

On the asymptotic behaviour of solutions of nonlinear integral equations in BANACH spaces

The asymptotic behaviour of solutions of nonlinear VOLTERRA integral equations is studied in a real BANACH spaces. The nonlinear operator is assumed to satisfy some accretivity-type conditions.