Oscillation and asymptotic behavior of solutions of linear differential inequalities and equations with deviating arguments (Q760577)

Sturmian comparison theorems are established for nonlinear differential inequalities with deviating arguments of the form \(y(t)[(R(t)y'(t))'+H(t,y<\sigma (t)>)]\leq 0\), \(t\geq t_ 0\) and \(y(t)[(r(t)y'(t))'+h(t,y<\xi (t)>)]\leq 0,\)t\(\geq t_ 0\) where \(z<\xi (t)>=(z[\xi_ 1(t)],...,z[\xi_ m(t)])\), \(\xi =(\xi_ 1,...,\xi_ m)\). Sufficient conditions are obtained under which every solution of the differential inequality \(y(t)[(r(t)y'(t))'+p(t)f(y[\tau (t)])]\leq 0,\) \(t\geq t_ 0\), is oscillatory or tends to zero as \(t\to \infty\).