-semigroups of linear operators on some ultrametric Banach spaces.
Cauchy problem for derivors in finite dimension.
Cauchy Problems for Polynomial Operator Matrices on Abstract Energy Spaces.
Classical solutions of parabolic equations in Hölder spaces
Sono dati nuovi teoremi di esistenza per soluzioni regolari di equazioni di evoluzione paraboliche astratte con applicazioni all'equazione del calore in spazi di funzioni holderiane e alle equazioni semilineari.
Closed semistable operators and singular differential equations
We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of -semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions to a singularly...
Coerciveness inequality for nonlocal boundary value problems for second order abstract elliptic differential equations.
Compact perturbations of linear differential equations in locally convex spaces
Herzog and Lemmert have proven that if E is a Fréchet space and T: E → E is a continuous linear operator, then solvability (in [0,1]) of the Cauchy problem ẋ = Tx, x(0) = x₀ for any x₀ ∈ E implies solvability of the problem ẋ(t) = Tx(t) + f(t,x(t)), x(0) = x₀ for any x₀ ∈ E and any continuous map f: [0,1] × E → E with relatively compact image. We prove the same theorem for a large class of locally convex spaces including: • DFS-spaces, i.e., strong duals of Fréchet-Schwartz spaces,...
Completeness of elementary solutions of second order elliptic equations in a semi-infinite tube domain.
Conjectures sur les équations différentielles -adiques linéaires
Continuity versus nonexistence for a class of linear stochastic Cauchy problems driven by a Brownian motion
Let denote the generator of the rotation group in the space , where denotes the unit circle. We show that the stochastic Cauchy problem where is a standard Brownian motion and is fixed, has a weak solution if and only if the stochastic convolution process has a continuous modification, and that in this situation the weak solution has a continuous modification. In combination with a recent result of Brzeźniak, Peszat and Zabczyk it follows that (1) fails to have a weak solution for all...
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