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Boundary-Value Problem for a Degenerate High-Odd-Order Equation

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We consider a boundary-value problem for a degenerate high-odd-order equation. The uniqueness of the solution is shown by the method of energy integrals. The solution is constructed by the method of separation of variables. In this case, we get the eigenvalue problem for a degenerate even-order ordinary differential equation. The existence of eigenvalues is proved by means of reduction to the integral equation.

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Correspondence to Yu. P. Apakov.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 10, pp. 1318–1331, October, 2014.

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Apakov, Y.P., Irgashev, B.Y. Boundary-Value Problem for a Degenerate High-Odd-Order Equation. Ukr Math J 66, 1475–1490 (2015). https://doi.org/10.1007/s11253-015-1039-7

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Keywords

  • Integral Equation
  • Eigenvalue Problem
  • Green Function
  • Fundamental Solution
  • Multiple Characteristic