Asymptotic behaviour of stochastic quasi dissipative systems
We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.
Asymptotic behaviour of strongly damped nonlinear hyperbolic equations
Asymptotic equivalence of impulsive differential equations in a Banach space.
By means of Schauder's fixed point theorem sufficient conditions for asymptotic equivalence of impulsive equations in a Banach space are found.
Asymptotic properties of solutions of a second order nonlinear delay differential equation
Asymptotically almost periodic and almost periodic solutions for a class of evolution equations.
Attractors for nonautonomous multivalued evolution systems generated by time-dependent subdifferentials.
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.
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 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 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.
Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces
In this paper, we present the existence result for Carathéodory type solutions for the nonlinear Sturm- Liouville boundary value problem (SLBVP) in Banach spaces on an arbitrary time scale. For this purpose, we introduce an equivalent integral operator to the SLBVP by means of Green’s function on an appropriate set. By imposing the regularity conditions expressed in terms of Kuratowski measure of noncompactness, we prove the existence of the fixed points of the equivalent integral operator. Mönch’s...
Coalescence of solutions for nonlinear Stieltjes equations.
Co-density and other properties of the solution set of differential inclusions with noncompact right-hand side
There are studied two classes of differential inclusions with right-hand side admitting noncompact values in a Banach space. Co-density, lower semicontinuity in initial point and relaxation property of the solution set have been obtained.