title: Existence of solutions of a two-dimensional boundary value problem for a system of nonlinear equations arising in growing cell populations.
abstract: In the paper [A. Ben Amar, A. Jeribi, and B. Krichen, Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberg's model type, to appear in Math. Slovaca. (2014)], the existence of solutions of the two-dimensional boundary value problem (1) and (2) was discussed in the product Banach space L(p)×L(p) for p∈(1, ∞). Due to the lack of compactness on L1 spaces, the analysis did not cover the case p=1. The purpose of this work is to extend the results of Ben Amar et al. to the case p=1 by establishing new variants of fixed-point theorems for a 2×2 operator matrix, involving weakly compact operators.
authors.affiliation: a Département de Mathématiques, Faculté des Sciences de Sfax , Université de Sfax , Route de Soukra Km 3.5, B.P. 1171, 3000 Sfax, unisie.
authors.forename: Aref
authors.initials: A
authors.lastname: Jeribi
authors.forename: Bilel
authors.initials: B
authors.lastname: Krichen
authors.forename: Bilel
authors.initials: B
authors.lastname: Mefteh
mesh_terms: D002455:Cell Division; D008433:Mathematics; D008954:Models, Biological; D017711:Nonlinear Dynamics