Fourth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 03, 1999, pp. 29-37.

A remark on the half-linear extension of the Hartman-Wintner theorem

Ondrej Dosly

Abstract:
We establish a Hartman-Wintner type theorem for the half-linear second order differential equation
$$ (r(t)\Phi_p(x'))'+c(t)\Phi_p(x)=0,\quad \Phi_p(x):=|x|^{p-2}x.$$
This equation is viewed as a perturbation of the non-oscillatory equation
$$ (r(t)\Phi_p(x'))'+\tilde c(t)\Phi_p(x)=0 $$
with $\tilde c(t)\ne 0$ eventually.

Published July 10, 2000.
Mathematics Subject Classifications: 34C10.
Key words: Half-linear equation, scalar p-Laplacian, Hartman-Wintner criterion.

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Ondrej Dosly
Mathematical Institute, Czech Academy of Sciences,
Zizkova 22, CZ-616 62 Brno
email: dosly@math.muni.cz

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