Abstract:
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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