On the stability of volterra integral equations with seperable kernels

Abstract

Conditions are derived for the uniform stability of a linear scalar Volterra integral equation of the second kind with a seperable (or Pincherle-Goursat) kernel. Certain qualitative behaviour of the solutions of linear systems of differential equations, such as uniform stability and monotonicity, essential for our analysis, are studied. Use is made of a representation of the resolvent kernel to relate the stability criteria directly in terms of the kernel of the integral equation. Extension of the results to a wider class of integral and integro-differential equations are discussed briefly.

AMS (MOS):

• 45,65