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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1998, Volume 63, Issue 6, Pages 882–890 (Mi mz1359)

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

Yu. D. Salmanov

N. Tusi Azerbaijan State Pedagogical University

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 $F(x)$.

DOI: https://doi.org/10.4213/mzm1359

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English version:
Mathematical Notes, 1998, 63:6, 777–784

Bibliographic databases:

UDC: 517.927.4

Citation: Yu. D. Salmanov, “Smoothness of generalized solutions of boundary value problems for certain degenerate nonlinear ordinary differential equations”, Mat. Zametki, 63:6 (1998), 882–890; Math. Notes, 63:6 (1998), 777–784

Citation in format AMSBIB
\Bibitem{Sal98} \by Yu.~D.~Salmanov \paper Smoothness of generalized solutions of boundary value problems for certain degenerate nonlinear ordinary differential equations \jour Mat. Zametki \yr 1998 \vol 63 \issue 6 \pages 882--890 \mathnet{http://mi.mathnet.ru/mz1359} \crossref{https://doi.org/10.4213/mzm1359} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1679221} \zmath{https://zbmath.org/?q=an:0917.34011} \transl \jour Math. Notes \yr 1998 \vol 63 \issue 6 \pages 777--784 \crossref{https://doi.org/10.1007/BF02312772} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000076726600031}