A nonlocal boundary value problem for systems of quasilinear hyperbolic equations

The nonlocal boundary value problem for second-order systems of quasilinear hyperbolic equations was analyzed. The coefficient sufficient conditions for the unique solvability of nonlocal boundary value problem was determined by introducing functions and applying solution of two-point boundary value problems for systems of ordinary differential equations. A parameterization method was developed to obtain conditions for the unique solvability of the problems. It was found that a family of two-point boundary value problems for the systems of ordinary differential equation can be obtained on varying x over [0, ω]. A nonlocal boundary value problem was found to be solvable if it has a unique solution v(t,x) for any functions F(t,x) and φ(t,x).