An integro-differential equation defined on a curve in the angular domain and containing a complex conjugate
EDN: SQLRSR
Abstract
A new linear integro-differential equation is studied on a closed curve located on the complex plane. There are some restrictions on the curve and the coefficients of the equation. The equation contains hypersingular integrals with the desired function. A characteristic feature of the equation is the presence of regular integrals with the desired function and its complex conjugate value. The solution of the equation is reduced to solving a mixed boundary value problem for analytic functions and the subsequent solutijn of differential equations with additional conditions on the solution. The conditions for the solvability of the original equation are explicitly stated. When these are performed, the solution is in closed form. An example is given.
References
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Review
For citations:
Shilin A.P. An integro-differential equation defined on a curve in the angular domain and containing a complex conjugate. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2025;33(2):103-113. (In Russ.) EDN: SQLRSR
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