Some Theorems in the Existence, Uniqueness and Stability solutions of Volterra Integrals Equations (original) (raw)
International Journal of Nonlinear Analysis and Applications, 2022
In this paper, utilizing the technique of Petryshyn’s fixed point theorem in Banach algebra, we analyze the existence of solution for functional integral equations, which includes as special cases many functional integral equations that arise in various branches of non-linear analysis and its application. Finally, we introduce the numerical method formed by modified homotopy perturbation approach to resolving the problem with acceptable accuracy.
On the Ulam Type Stability of Nonlinear Volterra Integral Equations
arXiv (Cornell University), 2021
In this paper, we examine the Hyers-Ulam and Hyers-Ulam-Rassias stability of solutions of a general class of nonlinear Volterra integral equations. By using a fixed point alternative and improving a technique commonly used in similar problems, we extend and improve some well-known results on this problem. We also provide some examples visualizing the improvement of the results mentioned.
Qualitative Properties of Nonlinear Volterra Integral Equations
2008
In this article, the contraction mapping principle and Liapunov's method are used to study qualitative properties of nonlinear Volterra equations of the form x(t) = a(t) Z t 0 C(t,s)g(s,x(s)) ds,t � 0. In particular, the existence of bounded solutions and solutions with various Lp properties are studied under suitable conditions on the functions involved with this equation.
EXISTENCE AND UNIQUENESS RESULTS FOR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
Advances in the Theory of Nonlinear Analysis and its Applications, 2020
This paper establishes a study on some important latest innovations in the existence and uniqueness results by means of Banach contraction xed point theorem for Caputo fractional Volterra-Fredholm integro-dierential equations with boundary condition. New conditions on the nonlinear terms are given to pledge the equivalence. Finally, an illustrative example is also presented.
Krasnosel’skii-type fixed point theorems with applications to Volterra integral equations
Fixed Point Theory and Applications, 2013
ABSTRACT In this paper we present some fixed point results for the sum S + T of two mappings where S is a strict contraction and T is not necessarily weakly compact and satisfies a new condition formulated in terms of an axiomatic measure of weak noncompactness. Our fixed point results extend and improve several earlier results in the literature. In particular, our results encompass the analogues of Krasnosel’skii’s and Sadovskii’s fixed point theorems for sequentially weakly continuous mappings and a number of their generalizations. Finally, an application to integral equations is given to illustrate the usability of the obtained results. MSC: 37C25, 40D05, 31B10.
Properties of solutions for nonlinear Volterra integral equations
Discrete and Continuous Dynamical Systems, 2003
Some properties of non-locally bounded solutions for Abel integral equations are given. The case in which there exists two non-trivial solutions for such equations is also studied. Besides, some known results about existence, uniqueness and attractiveness of solutions for some Volterra equations are improved.
Cubo (Temuco), 2015
In this paper we prove existence and uniqueness of the solutions for a kind of Volterra equation, with an initial condition, in the space of the continuous functions with bounded variation which take values in an arbitrary Banach space. Then we give a parameters variation formula for the solutions of certain kind of linear integral equation. Finally, we prove exact controllability of a particular integral equation using that formula. Moreover, under certain condition, we find a formula for a control steering of a type of system which is studied in the current work, from an initial state to a final one in a prescribed time. En este trabajo probamos existencia y unicidad de las soluciones para una ecuación de Volterra, con condición inicial, en el espacio de funciones continuas con variación acotada y valores en un espacio de Banach arbitrario. Damos una formula de variación de parámetros para las soluciones de cierta clase de ecuación lineal integral. Finalmente probamos la controlabilidad exacta de una ecuación integral particular usando esa formula. Más aún, bajo cierta condición, encontramos una formula para una dirección de control de un tipo de Sistema que se estudia en el presente trabajo, desde un estado inicial a uno final en un tiempo prescrito. Keywords and Phrases: Existence and uniqueness of solutions of integral equations in Banach spaces; continuous functions; bounded variation norm; parameters variation formula; controllability.