Khoma-Mohyl's'ka S. Periodic boundary-value problems for the second order hyperbolic equations

The thesis deals with comprehensive research for solutions of the periodic boundary-value problems for the second order hyperbolic equations. Conditions of solvability for these problems are established. Exact classic pi, 2pi and 4pi - periodic solutions of the periodic boundary-value problems are found. A new scheme for investigation of the boundary-value problems solutions is proposed. It allows investigating of solutions of nonlinear boundary-value problems for the second order hyperbolic equation. The existence of generalized uninterrupted solutions of the 2pi-periodic boundary-value problems is proved. The obtained results are to be applied for investigation of the periodic general boundary-value problems. The existence of smooth solutions of the quasi-linear periodic boundary-value problems is proved.