Tsynajko P. Solutions of two point and boundary-value problems for second-order hyperbolic equations

In disertation the periodical problem for second-order l inear in homogeneous hyperbolic equation is considered. On the basis of solution of linear periodical problems obtained in two. Section the exact solution of two-point problem for second-order linear hyperbolic equation in class of continuous and diferentiated functions is established. Theorems of existence and uniqueness of solution proved. formulas of exact solutions of boundary-value are problems are established first. Theorems of existence and uniqueness of named problems are proved. Properties of operators , which give rise to solutions of linear boundary-value problems are studied. On the basis of it the conditions of existence of smooth solutions of boundary- value problems for two types of second-order quasilinear hyperbolic equation are esteblished.