On solvability of a Boussinesq type integro-differential equation with nonlocal integral conditions
T. K. Yuldashev K. H. Shabadikov1
|This article considers the questions of one value solvability of the nonlocal boundary value problem for a nonlinear Boussinesq type fourth-order integro-differential equation. The Fourier method of separation of variables is employed. The countable system of nonlinear integral equations (CSNIE) is obtained. To prove the theorem of one-value solvability of CSNIE the method of successive approximations is used. The convergence of the Fourier series to an unknown function of considering nonlocal boundary value problem is shown. This paper advances the theory of Boussinesq type differential equations.
|Boundary value problem, nonlinear equation, Boussinesq type equation, nonlocal integral conditions, one valued solvability
1Associate professor of Higher Mathematics Chair, M. F. Reshetnev Siberian State Aerospace University, Krasnoyarsk, firstname.lastname@example.org
2Associate professor of Mathematical Analyses and Differential Equations Chair, Fergana State University, Fergana, Uzbekistan
Citation: T. K. Yuldashev K. H. Shabadikov, "[On solvability of a Boussinesq type integro-differential equation with nonlocal integral conditions ]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:2 (2016) 72–84 (In Russian)