a1 Department of Mathematics, Rutgers, The State University of New Jersey, U.S.A.
We consider differential-delay equations which can be written in the form
The functions fi and gk are all assumed odd. The equation
is a special case of such equations with q = N + 1 (assuming f is an odd function). We obtain an essentially best possible theorem which ensures the existence of a non-constant periodic solution x(t) with the properties (1) x(t)≧0 for 0≦t≦q, (2) x(–t) = –x(t) for all t and (3) x(t + q) = –x(t) for all t. We also derive uniqueness and constructibility results for such special periodic solutions. Our theorems answer a conjecture raised in .
(Received September 09 1977)
† Partially supported by a grant from the National Science Foundation.
‡ Work carried out while a Visiting Member at the Courant Institute of Mathematical Sciences.