In this paper we prove existence results for first and second order semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces and nonlocal conditions, via a Nonlinear Alternative for condensing maps. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families. Mathematics subject clas...

In the present paper we are dealing with generation of analytic semigroups in the space of continuous and bounded functions by suitable second order differential operators, which have unbounded coefficients and may be degenerate. This means that we are away from the classical framework in the study of the generation of analytic semigroups by elliptic operators (see Lunardi [25] for a comprehens...

The power (−A)b, b ∈ C is defined for a closed linear operator A whose resolvent is polynomially bounded on the region which is, in general, strictly contained in an acute angle. It is proved that all structural properties of complex powers of densely defined operators with polynomially bounded resolvent remain true in the newly arisen situation. The fractional powers are considered as generato...

An intriguing feature of positive $C_0$-semigroups on function spaces (or more generally Banach lattices) is that their long-time behaviour much easier to describe than it for general semigroups. In particular, the convergence semigroup operators (strongly or in operator norm) as time tends infinity can be characterized by a set simple spectral and compactness conditions. present paper, we show...

We study continuity and Hölder of t ? P f $t\mapsto P_tf$ , where $P_t$ is a generalized Mehler semigroup in C b ( X ) $C_b(X)$ the space continuous bounded functions from Banach to R $\mathbb {R}$ ? $f\in C_b(X)$ . The generators L such semigroups are realizations class differential pseudo-differential operators, both finite infinite dimension. Examples operators which this theory applicable i...

We generalize results concerning C0-semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving C0-semigroup is local. Some basic properties of local operators are also given. We investigate cases where local operators generate local C0-semigroups, by using Taylor series or Yosida approximations. As norms we consider regular norm...

It is shown that, for the spectral operators of scalar type, the well-known characterizations of the generation of C0and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup being that of the exponentials of the operator.