Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

A nonlinear singularly perturbed Volterra integrodifferential equation of nonconvolution type

G. S. Jordana1

a1 University of Tennessee, Knoxville, Tenn., U.S.A.

Synopsis

We consider the nonconvolution initial value problem

S030821050001026X_eqn1

where μ is a small positive parameter, b(t, s) is a given real kernel, and F, g are given real functions. For the convolution case b(t,s) = a(t − s). Lodge, McLeod, and Nohel recently established many qualitative properties of the solution of (+); we extend their results to the general nonconvolution problem. In particular, conditions are given that ensure that the solution of (+) decreases to a limiting value α(μ) > 1 as t → ∞.

(Received July 08 1977)

Footnotes

† Research supported in part by a University of Tennessee Research Grant.