On solvability of a mixed problem for fredholm integro-differential equation of fourth order with degenerate kernel
T. K. Yuldashev1
| Annotation | It is studying the one value solvability of a mixed value problem for a nonlinear partial Fredholm integro-differential equation of the fourth order with degenerate kernel. It is developed the method of degenerate kernel to the case of partial Fredholm integro-differential equations of the fourth order. A distinctive feature of this work is that it was possible to obtain an approximate calculation formula for solving the considering mixed value problem. The nonlinear mixed value problem is reduced to a system of integral equations with complex right-hand side. The system of integral equations is considered as a system of algebraic equations under certain condition. It is founded a method for solving the system of algebraic equations that can be identify unknown functions in the right-hand side of the system. It is obtained the nonlinear Volterra integral equation of the second kind with respect to the second argument. It is proved the theorem of one value solvability of the mixed value problem for a nonlinear partial Fredholm integro-differential equation of the fourth order with degenerate kernel. In this it is used the method of successive approximations. |
|---|---|
| Keywords | mixed value problem, integro-differential equation, Fredholm type equation. degenerate kernel, system of algebraic equations, one valued solvability |
1Associate professor of Higher Mathematics Chair, M. F. Reshetnev Siberian State Aerospace University, Krasnoyarsk, tursunbay@rambler.ru
Citation: T. K. Yuldashev, "[On solvability of a mixed problem for fredholm integro-differential equation of fourth order with degenerate kernel]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,17:3 (2015) 66–74 (In Russian)
