Oscillation theorems for differential equations with a nonlinear damping term
The authors investigate oscillatory properties of the nonlinear second-order differential equation \[ (r(t)k_1(x,x'))' +p(t)k_2(x,x')x'+q(t)f(x)=0,\tag{*} \] under natural restrictions on the functions \(r,k_1,k_2,p,q\) and \(f\). Using a modified \(H\)-function averaging technique introduced for linear equations by \textit{Ch. G. Philos} [Arch. Math. 53, 482-492 (1989; Zbl 0661.34030)], additional conditions are found which guarantee that (*) possesses no nonoscillatory solution. The results of the paper are illustrated by a number of examples showing that the obtained criteria apply in situations where known criteria fail.
scientific article; zbMATH DE number 1915737
scientific article