Electronic Journal of Differential Equations,
Vol. 2015 (2015), No. 220, pp. 1-14.
Title: Oscillation constant for modified Euler type half-linear equations
Authors: Petr Hasil (Masaryk Univ., Brno, Czech Republic)
Michal Vesely (Masaryk Univ., Brno, Czech Republic)
Abstract:
Applying the modified half-linear Prufer angle, we study oscillation
properties of the half-linear differential equation
$$
[ r(t) t^{p-1} \Phi(x')]' + \frac{s(t)}{t \log^pt} \Phi(x) = 0, \quad
\Phi(x)=|x|^{p-1}\hbox{sgn} x.
$$
We show that this equation is conditionally oscillatory in a very general case.
Moreover, we identify the critical oscillation constant
(the borderline depending on the functions r and s which separates
the oscillatory and non-oscillatory equations).
Note that the used method is different from the standard method based
on the half-linear Prufer angle.
Submitted March 16, 2015. Published August 24, 2015.
Math Subject Classifications: 34C10, 34C15.
Key Words: Half-linear equations; Prufer angle; oscillation theory;
conditional oscillation; oscillation constant.