Geodesic
Smoothness of generalized solutions of boundary value problems for certain degenerate nonlinear ordinary differential equations
Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 882-890.

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The variational method is applied to the study of a boundary value problem of the first kind for a class of nonlinear ordinary differential equations of order $2r$ with strong degeneracy at the endpoints of the interval $(a,b)$. An inequality is obtained in which the norm of the solution $U$ of the problem under study in the sense of $W_{p,\alpha}^r(a,b)$ is estimated from above by the norms of the given functions $\Phi(x)$ and $F(x)$. 
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Yu. D. Salmanov. Smoothness of generalized solutions of boundary value problems for certain degenerate nonlinear ordinary differential equations. Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 882-890. http://geodesic.mathdoc.fr/item/MZM_1998_63_6_a9/

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