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 (−∞;∞). 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. Keywords: Inverse problem; First-Order problem, Second-Order problem, c0−semigroup, Periodic Solution. Joint work with: Mohammed AL Horani; Mauro Fabrizio; Hiroki Tanabe