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Mat. Sb. (N.S.), 1976, Volume 99(141), Number 4, Pages 548–558 (Mi msb2773)  

On approximate methods of solving nonlinear boundary value problems with a small parameter

L. A. Kalyakin


Abstract: Variational inequalities with a small parameter are considered, together with closely related nonlinear operator equations. The penalty method as applied to variational inequalities is studied, and Galerkin's method relative to nonlinear equations. Under conditions of monotonicity, coerciveness and hemicontinuity on the operators, uniform convergence (with respect to the small parameter) of the approximate solutions thus obtained to the exact solution is demonstrated.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Sbornik, 1976, 28:4, 491–500

Bibliographic databases:

UDC: 517.948
MSC: Primary 47H15; Secondary 65J05
Received: 17.03.1975

Citation: L. A. Kalyakin, “On approximate methods of solving nonlinear boundary value problems with a small parameter”, Mat. Sb. (N.S.), 99(141):4 (1976), 548–558; Math. USSR-Sb., 28:4 (1976), 491–500

Citation in format AMSBIB
\Bibitem{Kal76}
\by L.~A.~Kalyakin
\paper On approximate methods of solving nonlinear boundary value problems with a~small parameter
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 99(141)
\issue 4
\pages 548--558
\mathnet{http://mi.mathnet.ru/msb2773}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=410494}
\zmath{https://zbmath.org/?q=an:0364.65040}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 28
\issue 4
\pages 491--500
\crossref{https://doi.org/10.1070/SM1976v028n04ABEH001665}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976EQ33200004}


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