On the Well-Posedness of a Two-Point Boundary-Value Problem for a System with Pseudodifferential Operators

Abstract

We investigate the problem of the well-posedness of a boundary-value problem for a system of pseudodifferential equations of arbitrary order with nonlocal conditions. The equation and boundary conditions contain pseudodifferential operators whose symbols are defined and continuous in a certain domain $H ⊂ ℝ_{σ}^m$. A criterion for the existence and uniqueness of solutions and for the continuous dependence of the solution on the boundary function is established.