Oscillation of modified Euler type half-linear differential equations via averaging technique

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Authors

HASIL Petr ŠIŠOLÁKOVÁ Jiřina VESELÝ Michal

Year of publication 2022
Type Article in Periodical
Magazine / Source Electronic Journal of Differential Equations
MU Faculty or unit

Faculty of Science

Citation
Web https://ejde.math.txstate.edu/Volumes/2022/41/hassil.pdf
Keywords Half-linear equations; linear equations; Prüfer angle; oscillation criterion; averaging technique
Description In this article, we analyze the oscillation behavior of half-linear differential equation (r(t)t^(p-1)Phi(x'))' + s(t)/(t log^p t) Phi(x) = 0, Phi(x) = |x|^(p-1) sgn x, p > 1. Applying the modified half-linear Prüfer 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.
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