On the existence and nonexistence of solutions of some quasilinear hyperbolic equations

摘要

We consider a special class of quasilinear hyperbolic equations of arbitrary order suggested by V.A. Galaktionov. For these equations, we prove the existence of solutions periodic in t 0 and consider an initial-boundary value problem for which we derive sufficient conditions for the nonexistence of a global solution in the natural energy space of solutions.