Geodesic
Weighted Hardy inequalities and their applications to oscillation theory of half-linear differential equations
Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 110-121.

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For the equation $$ \left(\rho(t)|y'(t)|^{p-2}y'(t)\right)'+v(t)|y(t)|^{p-2}y(t)=0,\quad t\in (a,b) $$ where $1$, we establish the properties of oscillation and nonoscillation. 
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R. Oinarov; S. Y. Rakhimova. Weighted Hardy inequalities and their applications to oscillation theory of half-linear differential equations. Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 110-121. http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a7/

[5] O. Dosly, P. Rehak, Half–linear differential equations, Math. Studies, 202, Elsevier Science, North-Holland, 2005 | MR | Zbl

[6] P. Drabek, A. Kufner, “Hardy inequality and properties of the quasilinear Sturm–Liouville problem”, Rend. Lincei Mat. Appl., 18 (2007), 125–138 | MR | Zbl

[7] A. A. Elbert, “Half-linear second order differential equation”, Colloq. Math. Soc. János Bolyai, 30 (1979), 153–180 | MR

[8] A. Gogatishvili, A. Kufner, L.-E. Persson, A. Wedestig, “An equivalence theorem for integral conditions related to Hardy's inequality”, Real Anal. Exchange, 29 (2003/2004), 867–880 | MR

[9] G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, Cambridge University Press, 1934

[10] A. Kufner, L. Maligranda, L.-E. Persson, The Hardy Inequality. About its History and some related results, Vydavatelsky Servis Publishing House, Pilsen, 2007 | MR | Zbl

[11] A. Kufner, L.-E. Persson, Weighted Inequalities of Hardy Type, Word Scientific, New Jersey, London, Singapore, Hong Kong, 2003 | MR | Zbl

[12] A. Kufner, L.-E. Persson, A. Wedestig, “A study of some constants characterizing the weighted Hardy inequality”, Orlicz Centenary Volume, Banach Center Publ., 64, Polish Acad. Sci., Warsaw, 2004, 135–146 | DOI | MR | Zbl

[13] V. M. Manakov, “On the best constant in weighted inequalities for Riemann–Liouville integrals”, Bull. London Math. Soc., 24 (1992), 442–448 | DOI | MR | Zbl

[14] J. D. Mirzov, “On some analogs of Sturm's and Kneser's theorems for non-linear systems”, J. Math. Anal. Appl., 53 (1976), 418–425 | DOI | MR | Zbl

[15] B. Muckenhoupt, “Hardy's inequality with weights”, Studia Math., 44 (1972), 31–38 | MR | Zbl

[16] K. Myrzataeva, R. Oinarov, “Nonoscillation of half–linear second order differential equation”, Math. Journal, 7:2 (2007), 72–82 (in Russian) | MR | Zbl

[17] R. Oinarov, “On weighted norm inequalities with three weights”, J. London Math. Soc. (2), 48:1 (1993), 103–116 | DOI | MR | Zbl

[18] B. Opic, A. Kufner, Hardy–type inequalities, Longman, Harlow, 1990 | MR | Zbl

[19] M. Otelbaev, Estimates of the spectrum of the Sturm–Liouville operator, Gylym, Alma-Ata, 1990 (in Russian) | Zbl

[20] L.-E. Persson, V. D. Stepanov, “Weighted integral inequalities with the geometric mean operator”, J. Inequal. Appl., 7:5 (2002), 727–746 | DOI | MR | Zbl

[21] G. A. Tomasseli, “A class of inequalities”, Boll. Un. Mat. Ital., 2 (1969), 622–631 | MR

[22] A. Wedestig, Weighted inequalities of Hardy–type and their limiting inequalities, PhD thesis, Luleå University of Technology, Department of Mathematics, 2003