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Jaroš, Jaroslav; Takaŝi, Kusano; Tanigawa, Tomoyuki

Nonoscillation theory for second order half-linear differential equations in the framework of regular variation. (English) Zbl 1047.34034

Result. Math. 43, No. 1-2, 129-149 (2003).
The authors study regularity properties implying nonoscillation of the solutions of the half-linear equation \[ (| y'|^{\alpha- 1}y')'+ q(t)| y|^{\alpha- 1}y= 0 \] with \(\alpha> 0\) and \(q\) positive and continuous on the half-axis \(t\geq 0\). 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 [V. Marić, Regular variation and differential equations. Lecture Notes in Mathematics 1726. Berlin: Springer-Verlag (2000; Zbl 0946.34001)].
Reviewer: Vojislav Marić (Novi Sad)

Cited in 1 Review
Cited in 32 Documents

MSC:

34C11 Growth and boundedness of solutions to ordinary differential equations
26A12 Rate of growth of functions, orders of infinity, slowly varying functions
34D05 Asymptotic properties of solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations

Keywords:

half-linear equation; regularly varying solutions; nonoscillation

Citations:

Zbl 0946.34001
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\textit{J. Jaroš} et al., Result. Math. 43, No. 1--2, 129--149 (2003; Zbl 1047.34034)
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References:

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