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The main idea of the method of generalized functions (GFM) in solving boundary value problems for differential equations is to switch from the original boundary value problem (BVP), in which a differential equation or a system of differential equations and boundary conditions are specified on the boundary of the region, the number of which depends on the order of the equations (for external boundary value problems are also given certain conditions at infinity) to differential equations in the space of generalized functions with the right-hand side containing singular generalized functions of the type simple, double, or more layers at the boundary of the domain of definition, the densities of which depend on the boundary values of the desired function and its derivatives.

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Basic Concepts of Generalized Functions Theory: Fundamental Solutions and Their Properties

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  • 发表日期：

    2026年

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  • Lyudmila Alexeyeva,
  • Aigulim Bayegizova

摘要

The main idea of the method of generalized functions (GFM) in solving boundary value problems for differential equations is to switch from the original boundary value problem (BVP), in which a differential equation or a system of differential equations and boundary conditions are specified on the boundary of the region, the number of which depends on the order of the equations (for external boundary value problems are also given certain conditions at infinity) to differential equations in the space of generalized functions with the right-hand side containing singular generalized functions of the type simple, double, or more layers at the boundary of the domain of definition, the densities of which depend on the boundary values of the desired function and its derivatives.