Nonlinear Leray-Schauder alternatives and application to nonlinear problem arising in the theory of growing cell population
type: Item
instance of: scholarly article
title: Nonlinear Leray-Schauder alternatives and application to nonlinear problem arising in the theory of growing cell population
zbMATH Open document ID: 1263.92044
author: Afif Ben Amar
published in: Central European Journal of Mathematics
publication date: 2012-01-16T00:00:00Z
review text: The author uses the Leray-Schauder theory in order to study existence and locality for the following biological model arising in the theory of growing cell populations: \[ \lambda\phi(a,l)+\frac{\partial\phi}{\partial a}+\sigma(a,l)\phi(a,l)=\int_{l_1}^{l_2}r(a,l,l',\phi(a,l'))dl' \] in the open rectangle \(D=(0,l)\times(l_1,l_2)\) where \(\sigma\in L^\infty(D)\) and \(\lambda\in\mathbb{C}\).
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 31A10
Mathematics Subject Classification ID: 92C37
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5997969
zbMATH Keywords: cell population dynamics
zbMATH Keywords: nonlinear boundary value problem
reviewed by: Christian Fenske
MaRDI profile type: Publication
full work available at URL: s11533-011-0039-6
OpenAlex ID: W2079452690
cites work: A Leray--Schauder alternative for weakly-strongly sequentially continuous weakly compact maps
cites work: On a generalization of the Schauder and Krasnosel'skii fixed points theorems on Dunford-Pettis spaces and applications
cites work: Some Fixed Point Theorems and Application to Biological Model
cites work: Leray-Schauder alternatives for weakly sequentially continuous mappings and application to transport equation
cites work: Q5533818
cites work: A mathematical study in the theory of dynamic populations
cites work: Q3688898
cites work: Compact operators in Banach lattices
cites work: Q3254057
cites work: Q5573683
cites work: Q5312447
cites work: Sur Les Applications Lineaires Faiblement Compactes D'Espaces Du Type C(K)
cites work: Q4202871
cites work: Q3027866
cites work: A nonlinear problem arising in the theory of growing cell populations
cites work: Q4069857
cites work: On a nonlinear stationary problem arising in transport theory
cites work: COMPACTNESS RESULTS FOR TRANSPORT EQUATIONS AND APPLICATIONS
cites work: A nonlinear boundary value problem arising in growing cell populations
cites work: Existence results for a generalized nonlinear Hammerstein equation on \(L_{1}\) spaces
cites work: Some fixed point theorems of the Schauder and the Krasnosel'skii type and application to nonlinear transport equations
cites work: A theory for the age and generation time distribution of a microbial population
cites work: On linear kinetic equations involving unbounded cross-sections
cites work: Structure of the fixed points sets of k-set-contractions
cites work: Fixed Point Theorems for Various Classes of 1-Set-Contractive and 1-Ball- Contractive Mappings in Banach Space
cites work: An Elementary Version of the Leray-Schauder Theorem
cites work: Neue Existenzsätze in der Theorie nichtlinearer Integralgleichungen
cites work: Q5516366
cites work: Q4332942
cites work: Q3706042
DOI: 10.2478/S11533-011-0039-6
description: scientific article; zbMATH DE number 5997969