Periodic Boundary Value Problem for a Linear Elliptic Equation of the Second Order in a Half-Plane

Abstract

© 2020, Pleiades Publishing, Ltd. Abstract: We study periodic boundary value problems for a second-order linear partial differentialequation with constant coefficients in a half-plane under various assumptions about the roots ofthe characteristic equation. If the imaginary parts of these roots are of the same sign, then weconsider a boundary value problem of the type of the Hilbert problem, and if they are of oppositesigns, then we consider a problem of the Dirichlet type. Necessary and sufficient solvabilityconditions are obtained, explicit formulas are given for the solutions of these problems, and thenumber of solutions of the corresponding homogeneous problems is found.