Asymptotic formulas for non-oscillatory solutions of perturbed half-linear Euler equation. (English) Zbl 1158.34027

Pátíková, Zuzana

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 10, 3281-3290 (2008).

Summary: We establish asymptotic formulas for non-oscillatory solutions of the half-linear second-order differential equation
\[ (\Phi(x'))'+\frac{\gamma}{t^p}\,\Phi(x)+c(t)\Phi(x')=0, \]
where this equation is viewed as a perturbation of the half-linear Euler equation.

MSC:

34C10

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

half-linear differential equation; half-linear Euler equation; half-linear Euler-weber equation; modified Riccati equation

References:

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