Linear differential equations in Banach spaces are systematically treated with the help of
Laplace transforms. The central tool is an “integrated version” of Widder's theorem …

Although mathematics ranks last in the Six Arts (rites, music, archery, chariot racing,
calligraphy and mathematics), it is used in the most practical issues and affairs. Maximally, it …

The theory of linear Volterra Integro-differental equations has been develo** rapidly in the
last three decades. This book provides an easy-to-read, concise introduction to the theory of …

Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed
problems-involved in a numerous mathematical models in physics, engineering, and finance …

This paper is concerned with characterizations of those linear, closed, but not necessarily
densely defined operators A on a Banach space E with nonempty resolvent set for which the …

This book presents an operator-theoretic approach to ill-posed evolution equations. It
presents the basic theory, and the more surprising examples, of generalizations of strongly …

This review paper is devoted to the numerical analysis of abstract differential equations in
Banach spaces. Most of the finite-difference, finite-element, and projection methods can be …

The main purpose of this chapter is to present a comprehensive semilinear theory that will
allow us to study the properties of solutions of the non-densely defined Cauchy problems …

It is well known that solutions to some equations from propagation of heat or waves in solid
state physics, such as wave functions satisfying the Schödinger equation with the potential …

We give sufficient conditions for wellposedness of the complete second order Cauchy
problem (1.1) u"(t)–Bu'(t)–Au (t)= 0; u (0)= r, u'(0)= y where A and B are closed operators on …