Non-oscillation of periodic half-linear equations in the critical case

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Authors	HASIL Petr VESELÝ Michal
Year of publication	2016
Type	Article in Periodical
Magazine / Source	Electronic Journal of Differential Equations
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	half-linear equations; Prüfer angle; oscillation theory; conditional oscillation; oscillation constant
Description	Recently, it was shown that certain Euler type half-linear differential equations with periodic coefficients 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 do not need to coincide.
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