A trace formula of a boundary value problem for the operator Sturm-Liouville equation.
A weak invariance principle and asymptotic stability for evolution equations with bounded generators.
Adaptive finite element methods for elliptic problems: Abstract framework and applications
We consider a general abstract framework of a continuous elliptic problem set on a Hilbert space V that is approximated by a family of (discrete) problems set on a finite-dimensional space of finite dimension not necessarily included into V. We give a series of realistic conditions on an error estimator that allows to conclude that the marking strategy of bulk type leads to the geometric convergence of the adaptive algorithm. These conditions are then verified for different concrete problems...
Adjoints of solution semigroups and identifiability of delay differential equations in Hilbert spaces.
Almost automorphic functions with values in -Fréchet spaces.
Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces.
Almost automorphic solutions to some differential equations in Banach spaces.
Almost automorphy of semilinear parabolic evolution equations.
Almost periodic solutions of higher order differential equations on Hilbert spaces.
Almost-periodicity in linear topological spaces and applications to abstract differential equations.
An Algebraic Approach to Implicit Evolution Equations
A Banach algebra homomorphism on the convolution algebra of integrable functions is the essence of Kisyński's equivalent formulation of the Hille-Yosida theorem for analytic semigroups. For the study of implicit evolution equations the notion of empathy happens to be more appropriate than that of semigroup. This approach is based upon the intertwining of two families of evolution operators and two families of pseudo-resolvents. In this paper we show that the Kisyński approach can be adapted to empathy...
An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces
A general existence and uniqueness result of Picard-Lindelöf type is proved for ordinary differential equations in Fréchet spaces as an application of a generalized Nash-Moser implicit function theorem. Many examples show that the assumptions of the main result are natural. Applications are given for the Fréchet spaces , , , , for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.
An Approximation Theorem for Second-Order Evolution Equations.
An averaging principle for stochastic evolution equations. II.
In the present paper integral continuity theorems for solutions of stochastic evolution equations of parabolic type on unbounded time intervals are established. For this purpose, the asymptotic stability of stochastic partial differential equations is investigated, the results obtained being of independent interest. Stochastic evolution equations are treated as equations in Hilbert spaces within the framework of the semigroup approach.
An equation in the left and right fractional derivatives of the same order
An inverse problem for a second-order differential equation in a Banach space.
Application de la théorie d'extrapolation pour la résolution des équations différentielles à retard homogènes.
Application of the Mean Ergodic Theorem to Certain Semigroups
Approximate solution of an inhomogeneous abstract differential equation
Recently, we have developed the necessary and sufficient conditions under which a rational function approximates the semigroup of operators generated by an infinitesimal operator . The present paper extends these results to an inhomogeneous equation .
Approximate solutions and error bounds for second order operator differential equations