Petr Hasil, Michal Vesely
Abstract:
Recently, it was shown that the Euler type half-linear differential equations
with periodic coefficients r and s are conditionally oscillatory and the
critical oscillation constant was found.
Nevertheless, the critical case remains unsolved.
The objective of this article is to study the critical case. Thus, we consider
the critical value of the coefficients and we prove that any considered
equation is non-oscillatory. Moreover, we analyze the situation when the
periods of coefficients r and s do not need to coincide.
Submitted September 3, 2015. Published May 13 2016.
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 | |
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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