The Cauchy dual subnormality problem via de Branges–Rovnyak spaces

The Cauchy Problem for Semilinear Parabolic Equations in Besov Spaces

In this paper we first give a unified method by introducing the concept of admissible triplets to study local and global Cauchy problems for semi-linear parabolic equations with a general nonlinear term in different Sobolev spaces. In particular, we establish the local well-posedness and small global well-posedness of the Cauchy problem for semi-linear parabolic equations without the homogeneou...

Nonlocal Cauchy Problem for Impulsive Differential Equations in Banach Spaces

where A is the infinitesimal generator of a strongly continuous semigroup of bounded linear operators T (t) on a Banach space X; f : [0, b]×X → X; 0 < t1 < t2 < · · · < tp < tp+1 = b; Ii : X → X, i = 1, 2, · · · , p are impulsive functions and g : PC([0, b];X) → X . During recent years, the impulsive differential equations have been an object of intensive investigation because of the wide possi...

Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces

Cauchy Problem for Dispersive Equations in Α-modulation Spaces

In this article, we consider the Cauchy problem for dispersive equations in α-Modulation spaces. For this purpose, we find a method for estimating uk in α-modulation spaces when k is not an integer, and develop a Strichartz estimate in M p,q which is based on semigroup estimates. In the local case, we that the domain of p is independent of α, which is also the case in the Modulation spaces and ...

$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework

In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...