Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 41, pp. 1-16.

Title: Oscillation of modified Euler type half-linear differential equations  via averaging technique
       
Authors: Petr Hasil (Masaryk Univ., Brno, Czech Republic)
         Jirina Sisolakova (Masaryk Univ., Brno, Czech Republic)
         Michal Vesely (Masaryk Univ., Brno, Czech Republic)

Abstract:    
In this article, we analyze the oscillation behavior of half-linear differential equation
$$
 \big( r(t) t^{p-1} \Phi(x')\big)' + \frac{s(t)}{t \log^pt} \Phi(x) = 0, \quad
 \Phi(x)=|x|^{p-1}\text{sgn} x, \quad p > 1.
$$
Applying the modified half-linear Prufer angle and a general averaging technique
over unbounded intervals, we prove an oscillation criterion for the studied equation.
We point out that the presented oscillation criterion is new even in the linear case
when p=2.

Submitted Submitted August 7, 2021. Published June 27, 2022.
Math Subject Classifications: 34C10, 34C15.
Key Words: Half-linear equations; linear equations; Prufer angle;
           oscillation criterion; averaging technique.