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Solution of a multipoint boundary-value problem for a system of linear ordinary differential equations with holomorphic coefficients

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Abstract

Necessary and sufficient conditions are established for the existence of a unique holomorphic solution of a boundary-value problem for a system of linear ordinary differential equations with holomorphic coefficients and general linear boundary conditions. A procedure for finding this solution is investigated.

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Literature cited

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    N. V. Azbelev, I. M. Smolin, and Z. B. Tsalyuk, “On an approximate method for constructing the Cauchy function,” Dokl. Akad. Nauk SSSR,135, No. 3, 479–482 (1960).

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    K. Ya. Latysheva and N. I. Tereshchenko, Lectures on the Analytical Theory of Differential Equations and Their Applications [in Russian], Kiev, Inst. Mat. Akad. Nauk UkrSSR, (1970).

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    V. A. Churikov, “A theory on a differential inequality for a linear system of ordinary differential equations,” Ukr. Mat. Zh.,39, No. 4, 538–543 (1987).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 1, pp. 125–128, January, 1990.

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Churikov, V.A. Solution of a multipoint boundary-value problem for a system of linear ordinary differential equations with holomorphic coefficients. Ukr Math J 42, 113–115 (1990). https://doi.org/10.1007/BF01066373

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Keywords

  • Boundary Condition
  • Differential Equation
  • Ordinary Differential Equation
  • Linear Boundary
  • Linear Ordinary Differential Equation