Direct and inverse problems for degenerate differential equations

We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We indicate sufficient conditions for existence and uniqueness of a solution. Periodic conditions are assumed to improve previous approaches on the abstract problem to work on ((-infty ,infty )). Related inverse problems are discussed, too. All general results are applied to some systems of partial differential equations. Inverse problems for degenerate evolution integro-differential equations might be described, too.