On initial-boundary value problems in bounded and unbounded domains for a class of nonlinear hyperbolic equations of the third order

For the nonlinear hyperbolic equationu(2,1)=f(x,t,u,u(1,0),u(2,0),u(0,1),u(1,1))u(2,1)=f(x,t,u,u(1,0),u(2,0),u(0,1),u(1,1)) problems on bounded solutions in a half strip and in a strip are studied. Unimprovable conditions of local and global solvability and unique solvability of these problems are established.