Linear Singular Parabolic Equations in Banach Spaces.
Linear Stieltjes integral equations in Banach spaces
Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces have been presented in [5]. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums (see e.g. [3]). It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. Here basic results concerning equations of the form x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a) are presented on the basis of...
Linear Stieltjes integral equations in Banach spaces. II. Operator valued solutions
This paper is a continuation of [9]. In [9] results concerning equations of the form x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a) were presented. The Kurzweil type Stieltjes integration in the setting of [6] for Banach space valued functions was used. Here we consider operator valued solutions of the homogeneous problem (t) = I +dt [A(s)](s) as well as the variation-of-constants formula for the former equation.
Linearized stability results in continuous interpolation spaces
L//p-оценки решений одной разностной краевой задачи.
Lyapunov numbers for a countable system of ordinary differential equations
Majoration effective et application
Majorization of -semigroups in ordered Banach spaces
We give criteria for domination of strongly continuous semigroups in ordered Banach spaces that are not necessarily lattices, and thus obtain generalizations of certain results known in the lattice case. We give applications to semigroups generated by differential operators in function spaces which are not lattices.
Maximal regular boundary value problems in Banach-valued function spaces and applications.
Maximal regularity and Hardy spaces
Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in -spaces
Maximal regularity for second order non-autonomous Cauchy problems
We consider some non-autonomous second order Cauchy problems of the form ü + B(t)u̇ + A(t)u = f(t ∈ [0,T]), u(0) = u̇(0) = 0. We assume that the first order problem u̇ + B(t)u = f(t ∈ [0,T]), u(0) = 0, has -maximal regularity. Then we establish -maximal regularity of the second order problem in situations when the domains of B(t₁) and A(t₂) always coincide, or when A(t) = κB(t).
Maximum Principles for Linear Difference-Differential Opeartors in Periodic Function Spaces.
Mixed monotone iterative technique for abstract impulsive evolution equations in Banach spaces.
Modal stabilizability and spectral synthesis
Moment sequences and abstract Cauchy problems
We give a new characterization of the solvability of an abstract Cauchy problems in terms of moment sequences, using the resolvent operator at only one point.
Multiple solutions for impulsive semilinear functional and neutral functional differential equations in Hilbert space.
New approach to streaming semigroups with multiplying boundary conditions.
New criteria for the existence of periodic and almost periodic solutions for some evolution equations in Banach spaces.
New spectral criteria for almost periodic solutions of evolution equations
We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...