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Zbl 1047.34034
Jaroš, Jaroslav; Takaŝi, Kusano; Tanigawa, Tomoyuki
Nonoscillation theory for second order half-linear differential equations in the framework of regular variation.
(English)
[J] Result. Math. 43, No. 1-2, 129-149 (2003). ISSN 1422-6383; ISSN 0378-6218/e

The authors study regularity properties implying nonoscillation of the solutions of the half-linear equation $$(\vert y'\vert^{\alpha- 1}y')'+ q(t)\vert y\vert^{\alpha- 1}y= 0$$ with $\alpha> 0$ and $q$ positive and continuous on the half-axis $t\ge 0$. Some necessary and sufficient conditions for the existence of such solutions are presented. The results generalize corresponding ones for the linear equation (when $\alpha= 1$) as proved in [{\it V. Marić}, Regular variation and differential equations. Lecture Notes in Mathematics 1726. Berlin: Springer-Verlag (2000; Zbl 0946.34001)].
MSC 2000:
*34C11 Qualitative theory of solutions of ODE: Growth, etc.
26A12 Rate of growth of functions of one real variable
34D05 Asymptotic stability of ODE
34C15 Nonlinear oscillations of solutions of ODE

Keywords: half-linear equation; regularly varying solutions; nonoscillation

Citations: Zbl 0946.34001

Cited in: Zbl 1240.34180

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