Došlý, Ondřej; Marek, Daniel Half-linear dynamic equations with mixed derivatives. (English) Zbl 1092.39004 Electron. J. Differ. Equ. 2005, Paper No. 90, 18 p. (2005). The authors consider the second order half-linear dynamic equation in a time scale \[ (r(t)\Phi(x^\Delta))^\nabla + c(t)\Phi(x) = 0, \tag{1} \] where \(\Phi(x)=| x| ^{p-2}x\), \(p > 1\), \(r(t)\) is continuous, \(r(t) \neq 0\), \(c(t)\) is ld-continuous. The authors suppose that a time scale \(T\) is unbounded above. Equation (1) is said to be nonoscillatory if there exists \(\alpha \in T\) such that (1) is disconjugate on \([\alpha, \beta]\) for every \(\beta > \alpha\). In the opposite case, (1) is said to be oscillatory. The authors establish a theorem which relates disconjugacy of (1) to solvability of a Riccati-type equation and positivity of a \(p\)-degree functional. Using this result, oscillation (nonoscillation) statements are proved. Reviewer: Gennadij Demidenko (Novosibirsk) Cited in 6 Documents MSC: 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis Keywords:dynamic equation on a time scale; oscillatory equation; nonoscillatory equation; Picone’s identity; Riccati-type equation; disconjugacy PDFBibTeX XMLCite \textit{O. Došlý} and \textit{D. Marek}, Electron. J. Differ. Equ. 2005, Paper No. 90, 18 p. (2005; Zbl 1092.39004) Full Text: EMIS