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Dirichlet Problem on the Half-Line for an Abstract Euler–Poisson–Darboux Equation Containing Powers of an Unbounded Operator

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Abstract

We consider an abstract Euler–Poisson–Darboux equation containing powers of an unbounded operator that is the generator of a Bessel operator function. Sufficient conditions for the unique solvability of the Dirichlet problem on the half-line are obtained. The question concerning the convergence of the solution to zero at infinity is investigated. Examples are given.

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  1. Belgorod State University, Belgorod, 308015, Russia

    A. V. Glushak

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Correspondence to A. V. Glushak.

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Translated by V. Potapchouck

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Glushak, A.V. Dirichlet Problem on the Half-Line for an Abstract Euler–Poisson–Darboux Equation Containing Powers of an Unbounded Operator. Diff Equat 59, 1356–1371 (2023). https://doi.org/10.1134/S0012266123010004X

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  • DOI: https://doi.org/10.1134/S0012266123010004X

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