Applied Physics and Mathematics Annotation << Back The application of integrated presentation to boundary problems G.F. Efimova N.G. Shmeleva The main focus of the study is unique solvability of generalized solutions of the Tricomi problem for the Lavrent’ev–Bicadze with real parameter, provided that the elliptic part of the boundary line at the approach to change the type of ends arbitrarily small semicircle arcs. To prove the existence problem is solved using the integral representation obtained in I.N. Vekua, V.I. Zhegalova, K.B. Sabitova used and the method of reducing boundary problems to a singular integral equation, which is the method of regularization Carleman–Vekua reduced to a Fredholm integral equation of the second kind. In the proof of uniqueness of the solution of the boundary value problem are used: 1) extremum principle for second order elliptic systems ; 2) the method of introducing new features and a new variable ; 3) the Laplace transform on the line type change. The results obtained are new and have a theoretical character. They can be used in the further development of the theory of boundary value problems for equations of mixed type, and were presented in the form of presentations at scientific conferences. Keywords: The generalized Tricomi equation of mixed type, boundary value problems, integral representation, the unique solvability of the proof, the theorem, the function. Contacts: E-mail: shmelyova-2010@yandex.ru Pp. 57-64.