Two-point boundary value problem for systems of pseudo-differential equations under boundary conditions containing pseudo-differential operators

This paper deals with a two-point boundary value problem for pseudodifferential equations and systems of second order under conditions containing operators. The need to consider operators is caused by two reasons, first, such appear more often in applied problems, second, considering equations, it possible achieve the well-posedness Schwartz space S its dual space.First, we scalar equation symbol belonging $C_{-\infty}^{\infty}$, consists infinitely differentiable functions polinomial growth. For this found condition which specific type well-posed S. In addition, an example differential-difference convolution-type pseudo-differential operator are given.Then system symbols from $C _ {-\infty} ^ {\infty}$. system, prove existence well posed Fourier transform reduction triangular form used proof. case, also give correct S.Thus, work proves that any equation, as there always $S$ space, while contain algorithm constructing indicated. They whose depend on equations.