Alin Pogan

On exponential h-expansiveness of semigroups of operators in Banach spaces

This paper introduces the concept of exponential h-expansiveness for semigroups of nonlinear operators, which is an extension of classical concept of exponential expansiveness. Following the idea of obtaining an unitary treatment for stability and expansiveness, necessary and sufficient conditions for exponential h-expansiveness are given. As particular cases, the variants for exponential expansiveness of some well-known stability results due to Datko, Pazy, Ichikawa, Rolewicz and Neerven are obtained.

Fredholm properties of radially symmetric, second order differential operators

We analyse Fredholm properties of radially symmetric second order systems in unbounded domains. The main theorem relates the Fredholm index to the Morse index at infinity. As a consequence, linear operators are Fredholm in exponentially weighted spaces for almost all weights. The result provides the basic tool for the analysis of perturbation and bifurcation problems in the presence of essential spectrum. We give a simple illustrative example, where we use the implicit function theorem to calculate the effect of a localised source term on a trimolecular chemical reaction-diffusion systems on the plane.

Instability of Radially-Symmetric Spikes in Systems with a Conserved Quantity

We show that radially symmetric spikes are unstable in a class of reaction-diffusion equations coupled to a conservation law.

ON

In this paper we investigate the most general dichotomy concept of evolutionary processes. This dichotomy concept includes many interesting situations, among them we note the nonuniform dichotomy. We characterize the

{\bf (a,b)}

(a,b)

-DICHOTOMY FOR EVOLUTIONARY PROCESSES ON A HALF-LINE

-dichotomy in terms of the admissibility of the pair

On the connection between the exponential stability of C0-semigroups and the admissibility of a certain Sobolev space

(L^1_a, L^{\infty}_b)

Generalizations of a Theorem of Datko and Pazy

. Also, generalizations of the results of [ 20 ], [ 23 ] are obtained.

(\( L^p, L^q \))-Admissibility and Exponential Dichotomy of Evolutionary Processes on the Half-line

Abstract Let T be a strongly continuous semigroup on a Banach space X and A its infinitesimal generator. We will prove that T is exponentially stable, if and only if, there exist p∈[1,∞) such that the space W p,1 0 ( R + ,X) is admissible to the system Σ(A,I,I), defined below (i.e for all f belonging to the Sobolev space W p,1 0 ( R + ,X), the convolution T ∗f lies in W p,1 0 ( R + ,X) .

DICHOTOMY AND FREDHOLM PROPERTIES OF EVOLUTION EQUATIONS

This note gives necessary and sufficient conditions for exponential stability of semigroups of linear operators in Banach spaces. Generalizations of a well-known result due to Datko, Pazy and Neerven are obtained for the case of semigroups of operators that are not strongly continuous.