Rocky Mountain Journal of Mathematics

Existence and Uniqueness of Global Solutions for a Size-Structured Model of an Insect Population with Variable Instar Duration

Hal L. Smith

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 24, Number 1 (1993), 311-334.

First available in Project Euclid: 5 June 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Smith, Hal L. Existence and Uniqueness of Global Solutions for a Size-Structured Model of an Insect Population with Variable Instar Duration. Rocky Mountain J. Math. 24 (1993), no. 1, 311--334. doi:10.1216/rmjm/1181072468.

Export citation


  • W. Alt, Periodic solutions of some autonomous differential equations with variable time delay, Proc. Conf. on Functional Differential Equations and Approx. of Fixed Points (Bonn, 1978), vol. 730, Springer, Berlin, Heidelberg, and New York, 1979.
  • K.L. Cooke, Functional-differential equations: some models and perturbation problems, in Differential equations and dynamical systems (J.K. Hale and J.P. La Salle, eds.), Academic Press, New York, 1967.
  • W.A. Coppel, Stability and asymptotic behavior of differential equations, D.C. Heath and Company, Boston, 1965.
  • J.A. Gatica and P. Waltman, A threshold model of antigen antibody dynamics with fading memory, in Nonlinear phenomena in mathematical sciences (V. Lakshmikantham, ed.), Academic Press, New York, 1982.
  • --------, Existence and uniqueness of solutions of a functional-differential equation modeling thresholds, Nonlinear Anal. T.M.A. 8 (1984), 1215-1222.
  • --------, A system of functional differential equations modeling threshold phenomena, Appl. Anal. 28 (1988), 39-50.
  • J.K. Hale, Theory of functional differential equations, Springer-Verlag, New York, Heidelberg, Berlin, 1977.
  • F.C. Hoppensteadt and P. Waltman, A flow mediated control model of respiration, Lectures on Mathematics in the Life Sciences 12 (1979), American Mathematical Society.
  • F. Hoppensteadt and P. Waltman, A problem in the theory of epidemics, Math. Biosci. 9 (1970), 71-91.
  • --------, A problem in the theory of epidemics II, Math. Biosc. 12 (1971), 133-145.
  • J.A.J. Metz and O. Diekmann, The dynamics of physiologically structured populations, Lecture Notes in Biomathematics 68 (1986), Springer Verlag, Berlin, Heidelberg, New York.
  • R.M. Nisbet and W.S.C. Gurney, The systematic formulation of population models for insects with dynamically varying instar duration, Theor. Population Biol. 23 (1983), 114-135.
  • H.L. Smith, Threshold delay differential equations are equivalent to standard FDE's, Equadiff 1991, International Conference on Differential Equations, Barcelona 1991 (C. Perelló, C. Simó, J. Solá-Morales, eds.), World Scientific Co., 1993, Vol. 2, 899-904.
  • H.L. Smith, Reduction of structured population models to threshold-type delay equations and functional differential equations. A case study, Mathematical Biosciences 113 (1993), 1-23.
  • P. Waltman, Deterministic threshold models in the theory of epidemics, Lecture Notes in Biomathematics 1 (1974), Springer Verlag.
  • P. Waltman and E. Butz, A threshold model for antigen antibody dynamics, J. Theor. Biol. 65 (1975), 499-512.