Direct and inverse problems for degenerate differential equations (Q1989475)

In this paper, the authors are concerned with the general abstract linear equations of the type: \[ BMu-Lu=f, \] where \(B\), \(M\) and \(L\) are closed linear operators in a complex Banach space \(E\), \(f\in E\) and \(u\) is the unknown, and their applications. They first establish sufficient conditions for the existence and uniqueness of a solution, both on the whole real axis and on the interval \([0,1]\). Related inverse problems are also discussed. Next, the authors apply the above equation, when \(B\) is the first and the second order differential operators in appropriate function spaces, to solve various degenerate first and second order differential equations.