Nonoscillatory functional-differential equations

Gerasimos E. Ladas, Y. G. Sficas and I. P. Stavroulakis

Vol. 115 (1984), No. 2, 391–398

DOI: 10.2140/pjm.1984.115.391

Abstract

Our aim in this paper is to obtain sufficient conditions under which certain functional differential equations have a “large” number of nonoscillatory solutions. Using the characteristic equation of a “majorant” delay differential equation with constant coefficients and Schauder’s fixed point theorem, we obtain conditions under which the functional differential equation in question has a nonoscillatory solution. Then a known comparison theorem is employed as a tool to demonstrate that if the functional differential equation has a nonoscillatory solution, then it really has a “large” number of such solutions.

Mathematical Subject Classification 2000

Primary: 34K15

Secondary: 34C10, 34C15

Milestones

Received: 6 April 1983

Revised: 31 January 1984

Published: 1 December 1984