Well-Posedness of Nonlocal Boundary-Value Problems and Schrödinger Equations

Questions related to the well-posedness of differential problems in the mathematical modeling of real objects, phenomena, and processes form are essential and very important part of problems of the description of real objects by mathematical means. Mathematically, a given boundary-value problem is said to be well-posed (in Hadamard sense) if (a) a solution exists, (b) the solution is unique, and (c) the solution is stable, that is, continuously depends on the data (initial and/or boundary conditions) of the problem. If at least one of these three conditions is violated, the problem is said to be ill-posed. In this chapter, we introduce the notion of well-posedness of nonlocal boundary-value problems for equations of Schrodinger type.