New oscillation criteria for third-order half-linear advanced differential equations

Abstract

The theme of this article is to provide some sufficient conditions for the asymptotic property and oscillation of all solutions of third-order half-linear differential equations with advanced argument of the form $${\left(r_2(t){\left({\left(r_1(t){\left(y^{\prime }(t)\right)}^{\alpha }\right)}^{\prime }\right)}^{\beta }\right)}^{\prime }+q(t)y^{\gamma }\left(\sigma (t)\right)=0,t\ge t_0>0,$$ where ${\int }^{\infty }{r}_1^{-\frac{1}{\alpha }}(s)\text{d}s<\infty$ and ${\int }^{\infty }{r}_2^{-\frac{1}{\beta }}(s)\text{d}s<\infty$. The criteria in this paper improve and complement some existing ones. The results are illustrated by two Euler-type differential equations.

25 pages