Integro-differential equation associated with the Riemann-Carleman boundary value problem
Abstract
We consider a linear integro-differential equation on a closed curve located on the complex plane. The coefficients of the equation have a special structure. The equation is first reduced to the mixed Riemann-Carleman boundary value problem for analytic functions. Next, two differential equations are solved in areas of the complex plane with additional conditions. The conditions for the solvability of the original equation are indicated explicitly. When they executed, the solution is given in closed form. An example is given
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Review
For citations:
Shilin A.P. Integro-differential equation associated with the Riemann-Carleman boundary value problem. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2024;32(2):73-81. (In Russ.)
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