TY  - JOUR
ID  - Došlý2006
LB  - Došlý2006
AU  - Došlý, Ondřej
TI  - A remark on the linearization technique in half-linear oscillation theory
ST  - A remark on the linearization technique in half-linear oscillation theory
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2006
VL  - 26
IS  - 2
SP  - 305
EP  - 315
DO  - http://dx.doi.org/10.7494/OpMath.2006.26.2.305
UR  - http://dx.doi.org/10.7494/OpMath.2006.26.2.305
AB  - We show that oscillatory properties of the half-linear second order differential equation \[(r(t)\Phi(x'))'+c(t)\Phi(x)=0,\qquad\Phi(x)=|x|^{p-2}x,\quad p\gt 1,\] can be investigated via oscillatory properties of a certain associated second order linear differential equation. In contrast to paper [O. Došlý, S. Peňa, A linearization method in oscillation theory of half-linear differential equations, J. Inequal. Appl. 2005 (2005), 235–245], we do not need to distinguish between the cases \(p\ge 2\) and \(p\in (1,2]\). Our results also improve the oscillation and nonoscillation criteria given in [O. Došlý, A. Lomtatidze, Oscillation and nonoscillation criteria for half-linear second order differential equations, to appear in Hiroshima Math. J.].
KW  - half-linear oscillation theory
KW  - oscillation and nonoscillation criteria
KW  - Riccati technique
KW  - perturbation principle
SN  - 1232-9274
ER  -