Non-oscillatory criteria for a class of second order non-linear forced neutral-delay differential equations

摘要

In this paper, sufficient conditions are obtained, so that the second order neutral delay differential equation $$ (r(t)(y(t) - p(t)y(t - au ))')' + q(t)G(y(h(t)) = f(t) $$ has a positive and bounded solution, where q, h, f a?? C ([0, a??), a??) such that q(t) a‰￥ 0, but a‰￠ 0, h(t) a‰¤ t, h(t) a?’ a?? as t a?’ a??, r a?? C (1) ([0, a??), (0, a??)), p a?? C (2) [0, a??), a??), G a?? C(a??, a??) and ?? a?? a??+. In our work r(t) a‰? 1 is admissible and neither we assume G is non-decreasing, xG(x) 0 for x a‰? 0, nor we take G is Lipschitzian. Hence the results of this paper improve many recent results.