Necessary and sufficient conditions for eventually vanishing oscillatory solutions of functional equations with small delays

Necessary and sufficient conditions are found for all oscillatory solutions of the equation (rn ￠ ’1(t)(rn ￠ ’2(t)( ￠ ’ ￠ ’ ￠ ’(r2(t)(r1(t)y ￠ € 2(t)) ￠ € 2) ￠ € 2 ￠ ’ ￠ ’ ￠ ’) ￠ € 2) ￠ € 2) ￠ € 2+a(t)h(y(g(t)))=b(t) to approach zero. Sufficient conditions are also given to ensure that all solutions of this equation are unbounded.