Periodic solutions of special differential equations: an example in non-linear functional analysis

1978/01/01 by Roger D. Nussbaum · 1 citation

paper · doi:10.1017/s0308210500010490

Abstract

Synopsis We consider differential-delay equations which can be written in the form The functions f i and g k 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 [8].

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