Stability and instability of equilibria of an equation of size structured population dynamics

Journal of Mathematical Analysis and Applications

Volumn 286, Issue 2, 2003, Pages 435-452

  Calsina, Àngel ^a   Sanchón, Manuel ^a  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

Equilibria; Size dependent population dynamics; Stability; Transcendental equation

Indexed keywords

EID: 0242593199     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00464-5     Document Type: Article

References (12)

1. A. Calsina, A nonlinear model for size-dependent population dynamics, in: C. Perelló, et al. (Eds.), International Conference on Differential Equations, Barcelona, 1991, World Scientific, 1993, pp. 345-351.
2. A. Calsina, J. Saldaña, A model of physiologically structured population dynamics with a nonlinear individual growth rate, J. Math. Biol. 33 (1995) 335-364.
3. Ph. Clément, O. Diekmann, M. Gyllenberg, H.J.A.M. Heijmans, H.R. Thieme, Perturbation theory for dual semigroups, Math. Ann. 277 (1987) 709-725.
4. Ph. Clément, O. Diekmann, M. Gyllenberg, H.J.A.M. Heijmans, H.R. Thieme, Nonlinear Lipschitz continuous perturbations in the sun-reflexive case, in: Volterra Integro Differential Equations in Banach Spaces and Applications, Trento, Italy, 1987, pp. 67-89.
5. J.B. Conway, Functions of One Complex Variable, Springer, New York, 1978.
6. K.L. Cooke, Z. Grossman, Discrete delay, distributed delay and stability switches, J. Math. Anal. Appl. 86 (1982) 592-627.
7. R. Datko, A procedure for determination of the exponential stability of certain differential-difference equations, Quart. Appl. Math. 36 (1978) 279-292.
8. W. Desch, W. Schappacher, Linearized stability for nonlinear semigroups, in: A. Favini, E. Obrecht (Eds.), Differential Equations in Banach Spaces, Springer, 1986, pp. 61-73.
9. A. Grabosch, H.J.A.M. Heijmans, Cauchy problems with state-dependent time evolution, Japan J. Appl. Math. 7 (1990) 433-457.
10. M.E. Gurtin, R.C. MacCamy, Nonlinear age dependent population dynamics, Arch. Rational Mech. Anal. 54 (1974) 281-300.
11. J. Pruss, Stability analysis for equilibria in age-specific populations dynamics, Nonlinear Anal. 7 (1983) 1291-1313.
12. G.F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, Dekker, New York, 1985.