Parallel theories of integral equations

  • T.A. Burton
  • John R. Haddock

Abstract

In this paper we show that we can offer a study of integral equations of the form $x(t)=a(t)-\int^t_0 C(t,s)[x(s)+G(s,x(s))]ds$ by placing conditions on either the first or the second coordinate of $C$. One obtains parallel theories yielding $L^{\infty}$ results by working with the second coordinate, or $L^1$ results by working with the first coordinate. Both lines of study are quite elementary.
Published
2010-08-25
Section
Articles