Continuous dependence for implicit differential equations in Banach spaces.
Contractivity in the Numerical Solution of Initial Value Problems.
Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria
It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...
Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria
It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...
Convoluted C-operator families and abstract Cauchy problems
Correction to our paper “Periodic solutions to abstract differential equations”
Corrigendum to Maximal regularity and Hardy spaces.
Criteria of correctness of linear boundary value problems for systems of generalized ordinary differential equations
Degenerate differential operators with parameters.
Dependence of a weak solution of the first order differential equation on a parameter.
Derivative of the norm of a linear mapping and its application to differential equations
In this paper the notion of the derivative of the norm of a linear mapping in a normed vector space is introduced. The fundamental properties of the derivative of the norm are established. Using these properties, linear differential equations in a Banach space are studied and lower and upper estimates of the norms of their solutions are derived.
Differential Equations in Operator Algebras. I. Invariance of the Siegel Disk.
Differential operators with non dense domain
Differential subordination results for new classes of the family .
Diffusion phenomenon for second order linear evolution equations
We present an abstract theory of the diffusion phenomenon for second order linear evolution equations in a Hilbert space. To derive the diffusion phenomenon, a new device developed in Ikehata-Matsuyama [5] is applied. Several applications to damped linear wave equations in unbounded domains are also given.
Discrete methods and exponential dichotomy of semigroups.
Empathy theory and the Laplace transform
This paper is concerned with double families of evolution operators employed in the study of dynamical systems in which cause and effect are represented in different Banach spaces. The main tool is the Laplace transform of vector-valued functions. It is used to define the generator of the double family which is a pair of unbounded linear operators and relates to implicit evolution equations in a direct manner. The characterization of generators for a special class of evolutions is presented.
Équations différentielles algébriques
Équations différentielles linéaires et majorations de multiplicités
Evolution operators for higher order abstract parabolic equations