[1]
|
D. M. Auslander, G. F. Oster and C. B. Huffaker, Dynamics of interacting populations, J. Franklin Inst., 297 (1974), 345-376.
|
[2]
|
G. Di Blasio, Nonlinear age-dependent population growth with history-dependent birth rate, Math. Biosci., 46 (1979), 279-291.
|
[3]
|
O. Diekmann, Ph. Getto and M. Gyllenberg, Stability and bifurcation analysis of Volterra functional equations in the light of suns and stars, SIAM J. Math. Anal., 39 (2007), 1023-1096.
|
[4]
|
O. Diekmann and M. Gyllenberg, Abstract delay equations inspired by population dynamics, Fun. Anal. Evol. Eq., 47 (2008), 187-200.
|
[5]
|
K. J. Engel, Operator matrices and systems of evolution equations, RIMS Kokyuroku, 966 (1996), 61-80.
|
[6]
|
K. J. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolution Equations," Springer, New York, 2000.
|
[7]
|
M. Farkas, On the stability of stationary age distributions, Appl. Math. Comp., 131 (2002), 107-123.
|
[8]
|
J. Z. Farkas, Stability conditions for a nonlinear size structured model, Nonl. Anal. (RWA), 6 (2005), 962-969.
|
[9]
|
J. Z. Farkas and T. Hagen, Stability and regularity results for a size-structured population model, J. Math. Anal. Appl., 328 (2007), 119-136.
|
[10]
|
J. Z. Farkas and T. Hagen, Linear stability and positivity results for a generalized size-structured Daphnia model with inflow, Appl. Anal., 86 (2007), 1087-1103.
|
[11]
|
J. Z. Farkas and T. Hagen, Asymptotic behavior of size-structured populations via juvenile-adult interaction, Discr. Cont. Dyn. Syst. B, 9 (2008), 249-266.
|
[12]
|
G. Fragnelli, A. Idrissi and L. Maniar, The asymptotic behavior of a population equation with diffusion and delayed birth process, Discr. Cont. Dyn. Syst. B, 7 (2007), 735-754.
|
[13]
|
G. Greiner, A typical Perron-Frobenius theorem with applications to an age-dependent population equation, Lect. Notes in Math., 1076 (1984), 86-100.
|
[14]
|
G. Greiner, Perturbing the boundary conditions of a generator, Houston J. Math., 13 (1987), 213-229.
|
[15]
|
B. Guo and W. Chan, A semigroup approach to age dependent population dynamics with time delay, Comm. PDEs, 14 (1989), 809-832.
|
[16]
|
T. Hagen, Eigenvalue asymptotics in isothermal forced elongation, J. Math. Anal. Appl., 224 (2000), 393-407.
|
[17]
|
T. Hagen and M. Renardy, Eigenvalue asymptotics in nonisothermal elongational flow, J. Math. Anal. Appl., 252 (2000), 431-443.
|
[18]
|
T. Hagen and M. Renardy, Studies on the linear equations of melt-spinning of viscous fluids, Diff. Int. Equ., 14 2001, 19-36.
|
[19]
|
M. Iannelli, "Mathematical Theory of Age-structured Population Dynamics," Giardini Editori, Pisa, 1994.
|
[20]
|
Y. Liu and Z.-R. He, Stability results for a size-structured population model with resources-dependence and inflow, J. Math. Anal. Appl., 360 (2009), 665-675.
|
[21]
|
A. J. Metz and O. Diekmann, "The Dynamics of Psyiologically Structured Populations," Springer, Berlin, 1986.
|
[22]
|
R. Nagel, The spectrum of unbounded operator matrices with non-diagonal domain, J. Funct. Anal., 89 (1990), 291-302.
|
[23]
|
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Springer, New York, 1983.
|
[24]
|
S. Pizzera, An age dependent population equation with delayed birth press, Math. Meth. Appl. Sci., 27 (2004), 427-439.
|
[25]
|
S. Pizzera and L. Tonetto, Asynchronous exponential growth for an age dependent population equation with delayed birth process, J. Evol. Equ., 5 (2005), 61-77.
|
[26]
|
J. W. Sinko and W. Streifer, A new model for age-size structure of a population, Ecology, 48 (1967), 910-918.
|
[27]
|
K. E. Swick, A nonlinear age-dependent model of single species population dynamics, SIAM J. Appl. Math., 32 (1977), 484-498.
|
[28]
|
K. E. Swick, Periodic solutions of a nonlinear age-dependent model of single species population dynamics, SIAM J. Math. Anal., 11 (1980), 901-910.
|
[29]
|
G. F. Webb, "Theory of Nonlinear Age-dependent Population Dynamics," Marcell Dekker, New York, 1985.
|