Geodesic
Half-linear Sturm--Liouville problem with weights: Asymptotic behavior of eigenfunctions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces and related problems of analysis, Tome 284 (2014), pp. 157-162.

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We consider a nonlinear Sturm–Liouville problem with weights. Under suitable assumptions on weights we prove an asymptotic estimate for the decay of the eigenfunctions. An application to the radial problem on the entire $\mathbb R^N$ is given. 
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Pavel Drábek; Alois Kufner; Komil Kuliev. Half-linear Sturm--Liouville problem with weights: Asymptotic behavior of eigenfunctions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces and related problems of analysis, Tome 284 (2014), pp. 157-162. http://geodesic.mathdoc.fr/item/TM_2014_284_a8/

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[5] Drábek P., Kuliev K., “Half-linear Sturm–Liouville problem with weights”, Bull. Belg. Math. Soc. Simon Stevin, 19:1 (2012), 107–119 | MR | Zbl