Asymptotic formulas for solutions of half-linear Euler-Weber equation

Z. Patikova, Tomas Bata University in Zlín, Zlín, Czech Republic

E. J. Qualitative Theory of Diff. Equ., Proc. 8'th Coll. Qualitative Theory of Diff. Equ., No. 15. (2008), pp. 1-11.

Abstract: 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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