Boundedness Properties of Solutions of Nonlinear Volterra Integral Equations
by
Jeffrey Neugebauer
University of Dayton
Coauthors: Muhammad Islam (University of Dayton)

Nonlinear Volterra integral equations of the form

x(t)=a(t)-

ó õ

t 0

C(t, s)g(s, x(s))  ds, t ≥ 0

(1) are studied using the contraction mapping principle as the primary mathematical tool. In particular, the existence of bounded solutions of these equations are found using various boundedness assumptions on a(t) and a'(t).

Date received: September 14, 2007