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Zbl 1128.34017
Došlý, Ondřej; Ünal, Mehmet
Half-linear differential equations: linearization technique and its application. (English)
[J] J. Math. Anal. Appl. 335, No. 1, 450-460 (2007). ISSN 0022-247X

Oscillatory properties of the half-linear second-order differential equation $$(k(t)\varphi(x'))'+c(t)\varphi(x)=0,\quad\varphi(x)=|x|^{p-2}x,\ p>1\tag 1$$ are investigated, and these properties are compared with the oscillatory behavior of a certain associated linear second-order differential equation. At the first, essentials of the half-linear oscillation theory are recalled and also some auxiliary technical results are presented. The main results of the paper are statements where oscillatory properties of (N) are compared with those of a certain associated linear equation. As a corollary, a conjecture posed by the first author in the paper [{\it O. Došlý}, Perturbations of the half-linear Euler-Weber differential equations, J. Math. Anal. Appl. 323, 426--440 (2006; Zbl 1107.34030)] is proved and some new research are formulated.
[Vasile Marinca (Timişoara)]

MSC 2000:: *34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: half-linear oscillation theory; oscillation and nonoscillation criteria; linearization technique; Riccati type equation; principal solution

Citations: Zbl 1107.34030

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