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Some fixed point theorems and existence of weak solutions of Volterra integral equation under Henstock-Kurzweil-Pettis integrability

Afif Ben Amar (2011)

Commentationes Mathematicae Universitatis Carolinae

In this paper we examine the set of weakly continuous solutions for a Volterra integral equation in Henstock-Kurzweil-Pettis integrability settings. Our result extends those obtained in several kinds of integrability settings. Besides, we prove some new fixed point theorems for function spaces relative to the weak topology which are basic in our considerations and comprise the theory of differential and integral equations in Banach spaces.

Subexponential Solutions of Linear Volterra Difference Equations

Martin Bohner, Nasrin Sultana (2015)

Nonautonomous Dynamical Systems

We study the asymptotic behavior of the solutions of a scalar convolution sum-difference equation. The rate of convergence of the solution is found by determining the asymptotic behavior of the solution of the transient renewal equation.

The existence of solutions to a Volterra integral equation

Wojciech Mydlarczyk (1996)

Annales Polonici Mathematici

We study the equation u = k∗g(u) with k such that ln k is convex or concave and g is monotonic. Some necessary and sufficient conditions for the existence of nontrivial continuous solutions u of this equation are given.

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