Pairs of function spaces and exponential dichotomy on the real line.
Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses
In this paper, we consider periodic solutions for a class of nonlinear evolution equations with non-instantaneous impulses on Banach spaces. By constructing a Poincaré operator, which is a composition of the maps and using the techniques of a priori estimate, we avoid assuming that periodic solution is bounded like in [1-4] and try to present new sufficient conditions on the existence of periodic mild solutions for such problems by utilizing semigroup theory and Leray-Schauder's fixed point theorem....
Periodic solutions for some partial functional differential equations.
Periodic systems dependent on parameters.
Periodicity and almost periodicity in Markov lattice semigroups
Periodicity of mild solutions to higher order differential equations in Banach spaces.
Perturbation theorems for local integrated semigroups and their applications
Motivated by a great deal of interest in operators that may not be densely defined and do not generate global integrated semigroups, we establish general perturbation theorems for local integrated semigroups and describe their applications to local complete second order abstract differential equations.
Perturbation theorems for maximal -regularity
Perturbations of bi-continuous semigroups
The notion of bi-continuous semigroups has recently been introduced to handle semigroups on Banach spaces that are only strongly continuous for a topology coarser than the norm-topology. In this paper, as a continuation of the systematic treatment of such semigroups started in [20-22], we provide a bounded perturbation theorem, which turns out to be quite general in view of various examples.
Point interactions in Lp .
Poisson's equation and characterizations of reflexivity of Banach spaces
Let X be a Banach space with a basis. We prove that X is reflexive if and only if every power-bounded linear operator T satisfies Browder’s equality = (I-T)XWe then deduce that X (with a basis) is reflexive if and only if every strongly continuous bounded semigroup with generator A satisfies . The range (I-T)X (respectively, AX for continuous time) is the space of x ∈ X for which Poisson’s equation (I-T)y = x (Ay = x in continuous time) has a solution y ∈ X; the above equalities for the ranges...
Positivity and stability for a system of transport equations with unbounded boundary perturbations.
Product integrals in strongly differentiate power associative groupoids.
Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations
In this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.
Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations
For any pair E,F of pseudotopological vector spaces, we endow the space L(E,F) of all continuous linear operators from E into F with a pseudotopology such that, if G is a pseudotopological space, then the mapping L(E,F) × L(F,G) ∋ (f,g) → gf ∈ L(E,G) is continuous. We use this pseudotopology to establish a result about differentiability of certain operator-valued functions related with strongly continuous one-parameter semigroups in Banach spaces, to characterize von Neumann algebras, and to establish...
Purely imaginary eigenvalues of operator semigroups.