-bounded semigroups and implicit evolution equations.
Banach function spaces and exponential instability of evolution families
In this paper we give necessary and sufficient conditions for uniform exponential instability of evolution families in Banach spaces, in terms of Banach function spaces. Versions of some well-known theorems due to Datko, Neerven, Rolewicz and Zabczyk, are obtained for the case of uniform exponential instability of evolution families.
Banach spaces
Boundary value problem for an infinite system of second order differential equations in spaces
The concept of measures of noncompactness is applied to prove the existence of a solution for a boundary value problem for an infinite system of second order differential equations in space. We change the boundary value problem into an equivalent system of infinite integral equations and result is obtained by using Darbo’s type fixed point theorem. The result is illustrated with help of an example.
Boundary value problem for differential inclusions in Fréchet spaces with multiple solutions of the homogeneous problem
The paper deals with the multivalued boundary value problem for a.a. , , in a separable, reflexive Banach space . The nonlinearity is weakly upper semicontinuous in . We prove the existence of global solutions in the Sobolev space with endowed with the weak topology. We consider the case of multiple solutions of the associated homogeneous linearized problem. An example completes the discussion.
Boundary value problems and controllability of linear systems with right invertible operators [Book]
Boundary value problems and periodic solutions for semilinear evolution inclusions
We consider boundary value problems for semilinear evolution inclusions. We establish the existence of extremal solutions. Using that result, we show that the evolution inclusion has periodic extremal trajectories. These results are then applied to closed loop control systems. Finally, an example of a semilinear parabolic distributed parameter control system is worked out in detail.
Boundary value problems for evolution inclusions
Boundary value problems for semilinear evolution inclusions: Carathéodory selections approach
In this paper we prove two existence theorems for abstract boundary value problems controlled by semilinear evolution inclusions in which the nonlinear part is a lower Scorza-Dragoni multifunction. Then, by using these results, we obtain the existence of periodic mild solutions.
Boundary value problems with nonlinear boundary conditions in Banach spaces
Bounded and periodic solutions of the Riccati equation in Banach space.
Bounded solutions of abstract equations.
Bounded solutions of second order semicoercive evolution equations in a Hilbert space and of nonlinear telegraph equations.
Bounded solutions on the Real line to non-autonomous Riccati Equations
Si dà un risultato di esistenza e unicità di una soluzione limitata in per un'equazione di Riccati infinito-dimensionale.
Brief survey of semigroup theory and its applications to evolution problems.
BV solutions of multivalued differential equations on closed moving sets in Banach spaces
This paper is concerned with the existence of BV and right continuous solutions for some classes of multivalued differential equations on closed moving sets in Banach spaces.
solutions of rate independent differential inclusions
We consider a class of evolution differential inclusions defining the so-called stop operator arising in elastoplasticity, ferromagnetism, and phase transitions. These differential inclusions depend on a constraint which is represented by a convex set that is called the characteristic set. For (bounded variation) data we compare different notions of solutions and study how the continuity properties of the solution operators are related to the characteristic set. In the finite-dimensional case...