Aymen Ammar

Stability of the S -essential spectra on a Banach space

In this paper, we give the characterization of S-essential spectra, we define the S-Riesz projection and we investigate the S-Browder resolvent. Finally, we study the S-essential spectra of sum of two bounded linear operators acting on a Banach space.

Stability of the S-left and S-right essential spectra of a linear operator

Abstract In the present paper, we define the S -left and the S -right essential spectra of a linear operator and we study the stability of the S -essential spectra on a Banach space.

A note on the essential pseudospectra and application

In this research article, we work with the notion of essential pseudospectra of closed, densely defined linear operators in the Banach space. We start by giving the definition and we investigate the characterization, the stability and some properties of these essential pseudospectra.

A Characterization of the Pseudo-Browder Essential Spectra of Linear Operators and Application to a Transport Equation

In this article, we study the pseudo-Browder essential spectra of densely closed, linear operators in Banach spaces. We start by giving the definition and we investigate the characterization, the stability, and some properties of pseudo-Browder essential spectra. Finally, we apply these results to a transport equation.

Some results on semi-Fredholm perturbations of multivalued linear operators

Abstract The upper and lower semi-Fredholm perturbations of multivalued linear operators were discussed in a previous paper by Álvarez et al. (J. Math Methods Appl Sci. 2014;37(5):620–644). The purpose of the present study is to investigate the and -Atkinson perturbation of linear relations. After that, we use the reached findings to establish a survey of results concerning various essential spectra of linear relations. We finish this paper by establishing some results of the essential spectra of a transport equations with abstract boundary conditions in -spaces.

Global Bifurcation from the Real Leading Eigenvalue of the Transport Operator

ABSTRACT The present paper deals with a nonlinear transport equation derived from a model introduced by Rotenberg (J. Theor. Biol., vol. 103, 1983, pp. 181–199), which describes the growth of a cell population. Each cell of this population is distinguished by its degree of maturation x and its maturation velocity y. We discussed some bifurcation results for a class of nonlinear transport operators under vacuum boundary conditions. Our results are based on the classical global bifurcation theorem of Rabinowitz type. Finally, some open problems are indicated.

ESSENTIALLY SEMI-REGULAR LINEAR RELATIONS

In this paper, we study the essentially semi-regular linear relation operators everywhere defined in Hilbert space. We establish a Kato-type decomposition of essentially semi-regular relations in Hilbert spaces. The result is then applied to study and give some properties of the Samuel-multiplicity.