A Note on Continuous Dependence of Solutions of Volterra Integral Equations (original) (raw)

A note on scalar Volterra integral equations, II

Journal of Mathematical Analysis and Applications, 1986

The scalar Volterra integral equation U(I) + ii g(f, s, u(s)) cis = f(t) is studied on bounded intervals and on the half line. Conditions are given such that solutions u depend in a Lipschitz continuous way on f in spaces f+",'([0, T], R). Also, conditions are given such that the operator (f(O), f'())H u() is order preserving. The results are applied to questions of uniform boundedness and asymptotic behavior of solutions. cl 1986 Academic Press, Inc.

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.

On Volterra-type integral equations in noncompact metric space

Journal of Inequalities and Applications, 2014

In the present work, we consider one of the possible generalizations of linear and nonlinear Volterra integral equations of the second kind in the case when the independent variable belongs to an arbitrary noncompact metric space. Sufficient conditions are obtained for the existence of solutions of Volterra-type integral equations in the nonhomogeneous case. Some applications of the obtained results to the integral inequalities are given. MSC: 35Q99; 35R35; 65M12; 65M70

On nonlinear scalar Volterra integral equations. I

Transactions of the American Mathematical Society, 1985

The scalar nonlinear Volterra integral equation \[ u ( t ) + ∫ 0 t g ( t , s , u ( s ) ) d s = f ( t ) ( 0 ⩽ t ) u(t) + \int _0^t {g(t,s,u(s))\,ds = f(t)\qquad (0 \leqslant t)} \] is studied. Conditions are given under which the difference of two solutions can be estimated by the variation of the difference of the corresponding right-hand sides. Criteria for the existence of lim u ( t ) \lim u(t) (as t → ∞ t \to \infty ) are given, and existence and uniqueness questions are also studied.

Solvability of Volterra-Stieltjes operator-integral equations and their applications

Computers & Mathematics with Applications, 2001

We investigate a class of operator-integral equations of Volterra-Stieltjes type and we study the solvability of those equations in the space of continuous functions. Equations in question create a generalization of numerous integral equations considered in nonlinear analysis. The main tool used in our considerations is the technique associated with measures of noncompactness. We show the applicability of our existence result in the study of a few integral equations of Volterra type.