On a size-structured population model with infinite states-at-birth and distributed delay in birth process

References

• Farkas , JZ and Hinow , P . 2010 . On a size-structured two-phase population model with infinite states-at-birth . Positivity , 14 ( 3 ) : 501 – 514 .
   Web of Science ®Google Scholar
• Farkas , JZ , Green , DW and Hinow , P . 2010 . Semigroup analysis of structured parasite populations . Math. Model. Nat. Phenomena , 5 : 94 – 114 .
   Web of Science ®Google Scholar
• Auslander , DM , Oster , GF and Huffaker , CB . 1974 . Dynamics of interacting populations . J. Franklin Inst. , 297 : 345 – 376 .
   Web of Science ®Google Scholar
• Piazzera , S and Tonetto , L . 2005 . Asynchronous exponential growth for an age dependent population equation with delayed birth process . J. Evol. Eqns , 5 : 61 – 77 .
   Web of Science ®Google Scholar
• Piazzera , S . 2004 . An age dependent population equation with delayed birth process . Math. Methods Appl. Sci. , 27 : 427 – 439 .
   Web of Science ®Google Scholar
• Farkas , JZ and Hinow , P . 2011 . Physiologically structured populations with diffusion and dynamic boundary conditions . Math. Biosci. Eng. , 8 : 503 – 513 .
   PubMed Web of Science ®Google Scholar
• Arina , O , Bertuzzi , A , Gandolfi , A , Sánchez , E and Sinisgalli , C . 2005 . The asynchronous exponential growth property in a model for kinetic heterogeneity of tumour cell populations . J. Math. Anal. Appl. , 302 : 521 – 542 .
   Web of Science ®Google Scholar
• Dyson , J , Villella-Bressan , R and Webb , GF . 2002 . Asynchronous exponential growth in an age structured population of proliferating and quienscent cells . Math. Biosci. , 177–178 : 73 – 83 .
   PubMed Web of Science ®Google Scholar
• Arina , O , Sánchez , E and Webb , GF . 1997 . Necessary and sufficient conditions for asynchronous exponential growth in age structured cell populations with quiescence . J. Math. Anal. Appl. , 215 : 499 – 513 .
   Web of Science ®Google Scholar
• Engel , K-J and Nagel , R . 2000 . One-parameter Semigroups for Linear Evolution Equations , New York : Springer .
   Google Scholar
• Clément , P , Heijmans , H , Angenent , S , van Duijin , C and de Pagter , B . 1987 . One-parameter Semigroups , North-Holland, Amsterdam : Elsevier Science Publishers B.V. .
   Google Scholar
• Arendt , W , Grabosch , A , Greiner , G , Groh , U , Lotz , HP , Moustakas , U , Nagel , R , Neubrander , F and Schlotterbeck , U . 1986 . One-parameter Semigroups of Positive Operators , Berlin : Springer-Verlag .
   Google Scholar
• Farkas , JZ and Hagen , T . 2009 . Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback . Commun. Pure Appl. Anal. , 8 : 1825 – 1839 .
   Web of Science ®Google Scholar
• Bai , M and Cui , S . 2012 . Analysis of a two-phase cell division model . Appl. Math. Comput. , 218 : 4849 – 4859 .
   Web of Science ®Google Scholar
• Thieme , HR . 1998 . Balanced exponential growth of operator semigroups . J. Math. Anal. Appl. , 223 : 30 – 49 .
   Web of Science ®Google Scholar
• Bátkai , A and Piazzera , S . 2001 . Semigroups and linear partial differential equations with delay . J. Math. Anal. Appl. , 264 : 1 – 20 .
   Web of Science ®Google Scholar
• Farkas , JZ and Hagen , T . 2007 . Stability and regularity results for a size-structured population model . J. Math. Anal. Appl. , 328 : 119 – 136 .
   Web of Science ®Google Scholar