ON THE WELL-POSEDNESS OF A TWO-POINT BOUNDARY-VALUE PROBLEM FOR A SYSTEM WITH PSEUDODIFFERENTIAL OPERATORS

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.