Nonlocal Boundary Value Problems for Linear Hyperbolic Systems with Two Independent Variables

Abstract

Nonlocal boundary value problems in a characteristic rectangle for second order linear hyperbolic systems are considered. There are established: (i) Unimprovable sufficient conditions for general boundary value problems to possess the Fredholm property; (ii) Optimal sufficient conditions of unique solvability of general boundary value problems; (iii) Effective sufficient conditions for doubly periodic problems to possess the Fredholm property; (iv) Unimprovable sufficient conditions of unique solvability of doubly periodic problems; (v) Effective sufficient conditions for boundary value problems of periodic type to possess the Fredholm property; (vi) Unimprovable sufficient conditions of unique solvability of boundary value problems of periodic type; (vii) Necessary and sufficient conditions of unique solvability of periodic and periodic type problems for linear hyperbolic systems with constant coefficients.