
This article is cited in 3 scientific papers (total in 3 papers)
An expression for the solution of a differential equation in terms of iterates of differential operators
A. V. Babin^{}
Abstract:
We obtain theorems on the expression of $A^{1}$ in terms of iterates of the operator $A$, which is the reproducing operator of a $1$parameter group of linear transformations of a Banach space, and whose spectrum does not surround $0$. These results are applied to first order differential equations with analytic coefficients and righthand sides (symmetric first order systems on a compact manifold without boundary), and to second order elliptic equations (equations with a real principal part on a manifold without boundary, selfadjoint equations degenerate on the boundary of the domain, and the Dirichlet problem for a selfadjoint equation in a domain with an analytic boundary). We obtain formulas expressing the value of the solution at a point in terms of the derivatives of the coefficients and the righthand side at this point.
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Mathematics of the USSRSbornik, 1978, 34:4, 411–424
Bibliographic databases:
UDC:
517.944
MSC: Primary 47A10, 47F05, 35J20; Secondary 47G05 Received: 03.06.1977
Citation:
A. V. Babin, “An expression for the solution of a differential equation in terms of iterates of differential operators”, Mat. Sb. (N.S.), 105(147):4 (1978), 467–484; Math. USSRSb., 34:4 (1978), 411–424
Citation in format AMSBIB
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\by A.~V.~Babin
\paper An expression for the solution of a~differential equation in terms of iterates of differential operators
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 105(147)
\issue 4
\pages 467484
\mathnet{http://mi.mathnet.ru/msb2535}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=496590}
\zmath{https://zbmath.org/?q=an:0382.350490442.35056}
\transl
\jour Math. USSRSb.
\yr 1978
\vol 34
\issue 4
\pages 411424
\crossref{https://doi.org/10.1070/SM1978v034n04ABEH001214}
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This publication is cited in the following articles:

A. V. Babin, “Fractional powers of a nonlinear analytic differential operator”, Math. USSRSb., 37:1 (1980), 9–38

A. V. Babin, “Solution of the cauchy problem with the help of weighted approximations of exponents by polynomials”, Funct. Anal. Appl., 17:4 (1983), 305–307

A. V. Babin, “Construction and investigation of solutions of differential equations by methods in the theory of approximation of functions”, Math. USSRSb., 51:1 (1985), 141–167

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