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Nonlocal Boundary Value Problem with an Integral Condition for a Mixed Type Equation with a Singular Coefficient

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Abstract

We study how a boundary value problem with a nonlocal integral condition of the first kind for a mixed type equation with a singular coefficient in a rectangular domain depends on a numerical parameter occurring in the equation. A uniqueness criterion is established, and theorems on the existence and stability of a solution of the problem are proved. The solution is constructed in closed form, and the convergence of the series in the class of regular solutions is justified.

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Notes

  1. To be definite, we assume that the coordinate system \(Oxy\) is right-handed.

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ACKNOWLEDGMENTS

This work was facilitated by the Moscow Center for Fundamental and Applied Mathematics.

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  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    N. V. Zaitseva

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  1. N. V. Zaitseva
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Correspondence to N. V. Zaitseva.

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Translated by V. Potapchouck

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Zaitseva, N.V. Nonlocal Boundary Value Problem with an Integral Condition for a Mixed Type Equation with a Singular Coefficient. Diff Equat 57, 210–220 (2021). https://doi.org/10.1134/S0012266121020105

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  • DOI: https://doi.org/10.1134/S0012266121020105

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