Boundary Value Problem for a Degenerate High-Order Equation with Singular Coefficients

Abstract The article considers a boundary value problem of the Dirichlet type for a degenerate equation of high even order with singular coefficients. The solution to the problem is constructed as a series in eigenfunctions of the spectral problem for a degenerate ordinary differential equation of high even order with lower-order terms. In this case, a boundary value problem for a one-dimensional differential equation of high even order with lower-order terms is also solved by reducing it to a Fredholm integral equation of the second kind. Sufficient conditions for the solvability and uniqueness of the problem are obtained.

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