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Journal of Biological Dynamics Volume 7, 2013 - Issue 1
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Original Articles

Existence of solutions of a two-dimensional boundary value problem for a system of nonlinear equations arising in growing cell populations

Aref JeribiDépartement de Mathématiques, Faculté des Sciences de Sfax, Université de Sfax, Route de Soukra Km 3.5, B.P. 1171, 3000 Sfax, unisieCorrespondence[email protected]
,
Bilel KrichenDépartement de Mathématiques, Faculté des Sciences de Sfax, Université de Sfax, Route de Soukra Km 3.5, B.P. 1171, 3000 Sfax, unisie
&
Bilel MeftehDépartement de Mathématiques, Faculté des Sciences de Sfax, Université de Sfax, Route de Soukra Km 3.5, B.P. 1171, 3000 Sfax, unisie
Pages 218-232 | Received 31 Aug 2012, Accepted 03 Jul 2013, Published online: 10 Oct 2013

References

  • R.P. Agarwal, D. O'Regan, and X. Liu, A Leray-Schauder alternative for weakly–strongly sequentially continuous weakly compact maps, Fixed Point Theory Appl. 1 (2005), pp. 1–10.
  • J. Appell and E. De Pascale, Su alcuni parametri connessi con la misura di non compattezza di Haussdorff in spazi di funzioni misurabili, Boll. Unione Mat. Ital. Sez. B (6) 3 (1984), pp. 497–515.
  • A. Ben Amar, A. Jeribi, and M. Mnif, Some fixed point theorems and application to biological model, Numer. Funct. Anal. Optim. 29 (2008), pp. 1–23. doi: 10.1080/01630560701749482
  • 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).
  • M. Boulanouar, Transport equations in cell population dynamics I, Electron. Differ. Equ. 144 (2010), pp. 1–20.
  • H. Brezis, Analyse Fonctionnelle, Théorie et Applications, Masson, Paris, 1983.
  • M. Cessenat, Théorèmes de trace Lp pour des espaces de fonctions de la neutronique, C. R. Acad. Sci. Paris Série I. 299 (1984), pp. 831–834.
  • M. Cessenat, Théorèmes de trace pour des espaces de fonctions de la neutronique, C. R. Acad. Sci. Paris Série I. 300 (1985), pp. 89–92.
  • S.N. Chow and J.K. Hale, Methods of Bifurcations Theory, Grundlehren der Mathematischen Wissenschaften 251, Springer-Verlag, New York, Berlin, 1982.
  • R. Dautray and J.L. Lions, Analyse mathématiques et calcul numérique pour les sciences et les techniques, Masson, Paris, 1988.
  • F.S. De Blasi, On a property of the unit sphere in Banach spaces, Bull. Math. Soc. Sci. Math. Roumanie 21 (1997), pp. 259–262.
  • N. Dunford and J.T. Schwartz, Linear Operators, Part I, General Theory, Interscience, New York, 1988.
  • M.A. Krasnosel'skii, Some problems of nonlinear analysis, Am. Math. Soc. Trans. Ser. 2 10(2) (1958), pp. 345–409.
  • K. Latrach and A. Jeribi, A nonlinear boundary value problem arising in growing cell populations, Nonlinear Anal. T.M.A. 36 (1999), pp. 843–862. doi: 10.1016/S0362-546X(97)00601-9
  • K. Latrach, M.A. Taoudi, and A. Zeghal, Some fixed point theorems of the Schauder and the Krasnosel'skii type and application to nonlinear transport equations, Differ. Equ. 221 (2006), pp. 256–271. doi: 10.1016/j.jde.2005.04.010
  • B. Lods, On linear kinetic equations involving unbounded cross-sections, Math. Methods Appl. Sci. 27 (2004), pp. 1049–1075. doi: 10.1002/mma.485
  • M. Rotenberg, Transport theory for growing cell populations, J. Theor. Biol. 103 (1983), pp. 181–199. doi: 10.1016/0022-5193(83)90024-3
  • D.R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge, 1980.

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