Third-order differential equations with multiple characteristics: degeneration and unknown external influence

Inverse problems of determination together with the solution of a degenerate differential equation with multiple characteristics of an unknown coefficient representing external influence (the free term) are studied. The nature of degeneration in the studied equation, as well as the type of the unknown coefficient, are determined by the time variable. Theorems of existence and uniqueness of regular solutions (solutions that possess all generalized derivatives according to S.L. Sobolev, which are involved in the equation) are proved for the studied problems.