Asymptotic behaviour of the nonoscillatory solutions of differential equations of second order with delay depending on the unknown function
The authors consider the nonlinear second-order delay differential equation of the form \[ (r(t)x'(t))'+ f(t,x(t),x(\Delta (t,x(t))))=0. \tag{1} \] Under certain assumptions on the functions \(r,\;f,\;\Delta\) they establish a classification of nonoscillatory solutions to (1) and present conditions for equation (1) to have a nonoscillatory solution of some type. Moreover, in the case when \(f\) is a strongly sublinear (superlinear) function conditions for the oscillation of each regular solution to (1) are stated.
second-order nonlinear differential equation with delay
scientific article; zbMATH DE number 1326340
scientific article