Inverse Problem for the Sobolev Type Equation of Higher Order

The article investigates the inverse problem for a complete, inhomogeneous, higher-order Sobolev type equation, together with Cauchy and overdetermination conditions. This was reduced to two equivalent problems in aggregate: regular singular. For these problems, theory of polynomially bounded operator pencils is used. unknown coefficient original equation restored using method successive approximations. main result this work theorem on unique solvability problem. study continues generalizes authors’ previous research area. All obtained results can be applied mathematical modeling various processes phenomena that fit under study.