Summary: This work is dedicated to the study of almost everywhere solution of one-dimensional mixed problem for one class of semi-linear fourth order equations. Conception of almost everywhere solution for mixed problem under consideration is introduced. In the conventional method, i.e. multiplication of the equation on the right function and subsequent relevant term by term integration (including some integration by parts), a theorem on a priori estimation of the solution almost everywhere under consideration of the mixed problem.

Key words: semi-linear equation, mixed problem, almost everywhere solution, a priori estimate.