The First Boundary Problem with an Integral Condition for a Mixed-Type Equation with a Characteristic Degeneration

Abstract

In this paper, we study the first boundary problem for a mixed-type elliptic-hyperbolic equation of the second kind in a rectangular domain. We construct the problem solution as the sum of a biorthogonal series and prove the uniqueness criterion for it. When proving the existence of the problem solution, we encounter the problem of small denominators. In this connection, we establish estimates for the separation of denominators from zero with the corresponding asymptotics; this allows us to justify the existence of a solution in the class of regular solutions.