Petr Hasil, Michal Vesely
Abstract:
Applying the modified half-linear Prufer angle, we study oscillation
properties of the half-linear differential equation
![$$
[ r(t) t^{p-1} \Phi(x')]' + \frac{s(t)}{t \log^pt} \Phi(x) = 0, \quad
\Phi(x)=|x|^{p-1}\hbox{sgn} x.
$$](gifs/aa.gif)
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.
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Petr Hasil Department of Mathematics and Statistics Faculty of Science, Masaryk University Kotlarska 2, CZ 611 37 Brno, Czech Republic email: hasil@mail.muni.cz |
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Michal Vesely Department of Mathematics and Statistics Faculty of Science, Masaryk University Kotlarska 2, CZ 611~37 Brno, Czech Republic email: michal.vesely@mail.muni.cz |
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