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

The authors study regularity properties implying nonoscillation of the solutions of the half-linear equation

(|y ' | α-1 y ' ) ' +q(t)|y| α-1 y=0

with α>0 and q positive and continuous on the half-axis t0. Some necessary and sufficient conditions for the existence of such solutions are presented. The results generalize corresponding ones for the linear equation (when α=1) as proved in [V. Marić, Regular variation and differential equations. Lecture Notes in Mathematics 1726. Berlin: Springer-Verlag (2000; Zbl 0946.34001)].


MSC:
34C11Qualitative theory of solutions of ODE: growth, boundedness
26A12Rate of growth of functions of one real variable, orders of infinity, slowly varying functions
34D05Asymptotic stability of ODE
34C15Nonlinear oscillations, coupled oscillators (ODE)
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