Abstract
Boundary value problems are considered for degenerating and nondegenerating differential equations of the Sobolev type with a nonlocal source as well as finite-difference methods for solving these problems. A priori estimates are derived for solving the problems posed in differential and difference interpretations. These a priori estimates entail the uniqueness and stability of the solution with respect to the initial data and the right-hand side on a layer as well as the convergence of the solution of each difference problem to that of the counterpart differential problem.
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