BOUNDARY VALUE PROBLEMS FOR COMPOSITE TYPE EQUATIONS WITH A QUASIPARABOLIC OPERATOR IN THE LEADING PART HAVING THE VARIABLE DIRECTION OF EVOLUTION AND DISCONTINUOUS COEFFICIENTS

It is studied the solvability of boundary value problems for non-classical differential equations of Sobolev type with an alternating function, which has a discontinuity of the first kind at the point zero. Also, this function changes sign depending on the sign of the variable x. It is proved the existence and uniqueness theorems for regular solutions, which has all generalizated derivatives including in this equation. Presence of necessary a priori estimates for the solutions of the problems under study.