Local estimates for modified Riccati equation in theory of half-linear differential equation

Abstract

In this paper we study the half-linear differential equation \begin{equation*} \bigl(r(t)\Phi_p(x')\bigr)'+c(t)\Phi_p(x)=0, \end{equation*} where $\Phi_p(x)=|x|^{p-2}x$, $p>1$. Using modified Riccati technique and suitable local estimates for terms in modified Riccati equation we derive new characterization of principal solution and new nonoscillation criteria.

Keywords

• half-linear differential equation
• nonoscillation criteria
• riccati equation
• principal solution