Lagrange formula conjugate third order differential equation

Abstract

The paper considers a boundary value problem for a third order with no smooth coefficients and pure derivatives. Odds. This is due to the fact to introduce the concept of the conjugate Green's function. It is very difficult to write the form of the conjugate differential operator corresponding to equation in the Lagrange sense. Therefore, in this work, without using strict conditions smoothness under the conditions and boundedness, an explicit form is found conjugate operator since the initial-boundary value problem for integral-differential equations has been studied based on the introduction special conjugate systems in the form of an integral-algebraic equations’ system. In this article, it can be said that Green's function is considered based on Lagrange's formula for the third-order differential equation with boundary conditions and its conjugate.