Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8409Research ArticleUniqueness of Solutions for One Class of Linear Equations of the First Kind with Two VariablesKadenovaZ AKadenova71@mail.ruMinistry of Education and Science of the Kyrgyz Republic150320133212908092016Copyright © 2013,2013This article is devoted to the study of the uniqueness of solutions of linear integral equations of the first kind with two independent variables in which the operator generated by the kernel, is not compact operator. The relevance of the problem is due to the needs in development of new approaches for the regularization and uniqueness of the solution of linear integral equations of the first kind with two independent variables. For approximate solutions of such tasks, stable to small variations of the initial data, we use the solutions derived by the method of regularization and belonging to the class of incorrectly formulated tasks. One of the classes of such ill-posed problems are integral equations of the first kind with two independent variables. The aim of the work is to prove the theorems of uniqueness for solving linear integral equations of the first kind with two independent variables. In the paper a theorem of the uniqueness of the solution of integral equations of the first kind with two independent variables is proved. To obtain the results formulated in the article the methods of functional analysis and method of nonnegative quadratic forms are used. The obtained results are new. The reliability of the result is set by prooves and illustrated by examples. The work has a theoretical character. The obtained theoretical results can be used in various fields of science and technology.linearinteqral equationsfirst kindtwo variablessolution and uniquenessлинейныйинтегральные уравненияпервого родадвух переменныхрешениеединственность[Aparstyn A.S. Nonclassical Linear Volterra Equations of the First Kind. — Utrecht: VSP, 2003.][Asanov A. Regularization, Uniqueness and Existence of Solutions of Volterra Equations of the First Kind. — Utrecht: VSP, 1998.][Bukhgeim A.L. Volterra Equations and Inverse Problems. — Utrecht: VSP, 1999.][Imanaliev M.I., Asanov A. On Solutions of Systems of Volterra Nonlinear Integral Equations of the First Kind // Doklady Akademii Nauk. — 1989. — Vol. 309, No 5. — Pp. 1052–1055.][Imanaliev M.I., Asanov A. On Solutions of Systems of Nonlinear Two Dimensional Volterra Integral Equations of the First Kind // Doklady Akademii Nauk. — 1991. — Vol. 317, No 2. — Pp. 330–333.][Lavrent’ev M.M., Romanov V.G., Shishatskii S.P. ILL-posed Problems of Mathematical Physics and Analysis. — American Mathematical Society: Providence, R.I, 1986.][Magnitskii N.A. Linear VolterrA Integral Equations of the First and Third Kind // Doklady Akademii Nauk. — 1991. — Vol. 317, No 2. — Pp. 330–333.][Shishatskii S.P., Asanov A., Atamanov E.R. Uniqueness Problems for Degenerating Equations and Nonclassical Problems. — Utrecht: VSP, 2001.]