On Constructing a Solution to a Boundary Value Problem for a Third-Order Inhomogeneous Equation Using the Green’s Function in Three-Dimensional Space

Key Points

• The research aims to construct a solution for a third-order non-homogeneous boundary value problem using Green's function.
• Applied the method of energy integrals to prove uniqueness of the solution.
• Used separation of variables to establish existence of a solution.
• Constructed the Green function to express the solution.
• Identified conditions for the functions ensuring regularity of solutions.
• Established the difference from zero of the 'small denominator' to justify uniform convergence.
• Proven uniqueness of solutions under specific conditions.
• Demonstrated existence of solutions using separation of variables.
• Provided explicit formulation of solutions in terms of the Green function.
• Outlined conditions that maintain the regularity of the solutions.