ON SOLVABILITY AND WELL-POSEDNESS OF BOUNDARY VALUE PROBLEMS FOR NONLINEAR HYPERBOLIC EQUATIONS OF THE FOURTH ORDER

In the rectangle Omega = [0, a] x [0, b] the nonlinear hyperbolic equation u((2,2)) = f(x, y, u) with the continuous right-hand side f : Omega x R -> R is considered. Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet-Nicoletti and Nicoletti boundary value problems are established.