Asymptotic formulas for solutions of half-linear Euler-Weber equation
We establish improved asymptotic formulas for nonoscillatory solutions of the half-linear Euler-Weber type differential equation $$ (\Phi(x'))'+\left[\frac{\gamma_p}{t^p}+\frac{\mu_p}{t^p\log^2 t}\right]\Phi(x)=0, \quad \Phi(x):=|x|^{p-2}x,\quad p>1 $$ with critical coefficients $$\gamm...
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Format: | Article |
Language: | English |
Published: |
University of Szeged
2008-07-01
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Series: | Electronic Journal of Qualitative Theory of Differential Equations |
Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=327 |
Summary: | We establish improved asymptotic formulas for nonoscillatory solutions of the half-linear Euler-Weber type differential equation
$$
(\Phi(x'))'+\left[\frac{\gamma_p}{t^p}+\frac{\mu_p}{t^p\log^2 t}\right]\Phi(x)=0, \quad \Phi(x):=|x|^{p-2}x,\quad p>1
$$
with critical coefficients
$$\gamma_p=\left(\frac{p-1}{p}\right)^p, \quad \mu_p= \frac{1}{2}\left(\frac{p-1}{p}\right)^{p-1},$$
where this equation is viewed as a perturbation of the half-linear Euler equation. |
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ISSN: | 1417-3875 |