Some comparison and oscillation results for first-order differential equations and inequalities with a deviating argument (Q1114845)

The authors investigate the interrelations between oscillatory properties and asymptotic behavior of the vector differential equation with deviating argument \(y'(t)+p(t)y(\tau (t))=0,\) its corresponding operator equation \(Y'(t)+p(t)Y(\tau (t))=0,\) and the scalar equation (in the case \(p:[t_ 0,\infty)\to {\mathbb{R}})\) \(x'(t)+p(t)x(\tau (t))=0,\) its nonlinear analogues, and corresponding differential inequalities with deviating argument. The theorems on existence of nonoscillatory solutions of nonlinear equations, which tend to some constant as \(t\to \infty\), are proved.