Oscillation criteria for second-order half-linear ordinary differential equations with damping
The authors state oscillation criteria for the second-order half-linear damped differential equation \[ (r(t)| y'(t)| ^{\alpha-1}y'(t))' +p(t)| y'(t)| ^{\alpha-1}y'(t) +q(t)| y(t)| ^{\alpha-1}=0,\quad t\geq t_0, \] where \(r\in C^1([t_0,\infty);(0,\infty))\), \(p,q\in C[t_0,\infty)\) and \(\alpha>0\). The obtained results are based on an averaging function and are closely related to the results of \textit{Q. Yang} and \textit{S. S. Cheng} [Georgian Math. J. 10, No. 4, 785--797 (2003; Zbl 1050.34043)] established independently.
half-linear second-order differential equation
scientific article; zbMATH DE number 2067058
scientific article