Asymptotic and oscillatory behavior of solutions of first order nonlinear neutral delay differential equations
The authors consider the (scalar) nonlinear neutral delay differential equation \([y(t)+p(t)y(t-\tau)]'-q(t)f(y(t-\sigma))=0,\) where \(q\geq 0\), \(\tau \geq 0\), \(\sigma \geq 0\) and \(uf(u)>0\), \(u\neq 0\). Two results giving hypotheses under which nonoscillatory solutions tend to zero as \(t\to \infty\) are proved. The novel feature (as compared to previous work) is that f is allowed to be nonlinear. Concerning the case where f is sublinear near the origin and superlinear at infinity it is shown, under certain additional conditions, that the equation considered is oscillatory.
nonlinear neutral delay differential equation
scientific article; zbMATH DE number 4210607
scientific article