Smoothness of generalized solutions of boundary value problems for certain degenerate nonlinear ordinary differential equations

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 solutionU of the problem under study in the sense ofW_p, ^r(a, b) is estimated from above by the norms of the given functions (x) andF(x).Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 882–890, June, 1998.