Smoothness of generalized solutions of boundary value problems for certain degenerate nonlinear ordinary differential equations
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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 solutionU of the problem under study in the sense ofW p, α r (a, b) is estimated from above by the norms of the given functions Φ(x) andF(x).
Key wordsvariational method boundary value problem of the first kind nonlinear ordinary differential equation Sobolev space coerciveness inequality
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- 1.S. M. Nikol'skii,Approximation of Functions of Several Variables and the Embedding Theorem [in Russian], 2nd edition, Nauka, Moscow (1977).Google Scholar