Geodesic
Zeros of derivatives of solutions to singular $(p,n-p)$ conjugate BVPs
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 137-141.

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Positive solutions of the singular $(p,n-p)$ conjugate BVP are studied. The set of all zeros of their derivatives up to order $n-1$ is described. By means of this, estimates from below of the solutions and the absolute values of their derivatives up to order $n-1$ on the considered interval are reached. Such estimates are necessary for the application of the general existence principle to the BVP under consideration.
Classification : 34B15, 34B16, 34B18
Keywords: singular conjugate BVP; positive solutions; zeros of derivatives; estimates from below 
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Rachůnková, Irena; Staněk, Svatoslav. Zeros of derivatives of solutions to singular $(p,n-p)$ conjugate BVPs. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 137-141. http://geodesic.mathdoc.fr/item/AUPO_2004__43_1_a13/