Perturbed generalized half-linear Riemann–Weber equation – further oscillation results

Abstract

We establish new oscillation and nonoscillation criteria for the perturbed generalized Riemann–Weber half-linear equation with critical coefficients \begin{equation*} (\Phi(x'))'+\left(\frac{\gamma_p}{t^p}+\sum_{j=1}^n\frac{\mu_p}{t^p\mbox{Log}_j^2 t}+\tilde{c}(t)\right)\Phi(x)=0 \end{equation*} in terms of the expression \begin{equation*} \frac{1}{\log_{n+1} t }\int^t \tilde{c}(s) s^{p-1}\mbox{Log}_n s \log_{n+1}^2 s \,{\rm d} s. \end{equation*} The obtained criteria complement results of [O. Došlý, Electron. J. Qual. Theory Differ. Equ., Proc. 10'th Coll. Qualitative Theory of Diff. Equ. 2016, No. 10, 1–14].

Keywords

• half-linear differential equation
• generalized riemann–weber equation
• (non)oscillation criteria
• perturbation principle