15
1. 3. 1988.
Oscillations of the sunflower equation
Consider the delay differential equation y(0 + ay(t) + Pf{y(t r)) = 0, (*) where a, /?, and r are positive constants and / is a continuous function such that uf(u) > 0 for u e [-A, B], 0, and lim = 1, v ; w—»o u where A and B are positive numbers. When /(«) = sinw, (*) is the so-called "sunflower" equation, which describes the motion of the tip of the sunflower plant. We obtain necessary and sufficient conditions for the oscillation of all solutions of (*), whose graph lies eventually in the strip R+ x [—A, B], in terms of the characteristic equation of the linearized equation z(t) + az(t) + f}z(t r) = 0.