References
Amann, H.: Dual semigroups and second order linear elliptic boundary value problems. Ist. J. Math.45, 225–254 (1983)
Butzer, P.L., Berens, H.: Semigroups of operators and approximations. Berlin, Heidelberg, New York: Springer 1967
Davies, E.B.: One-parameter semigroups. London: Academic Press 1980
Desch, W., Schappacher, W.: On relatively bounded perturbations of linearC 0-semigroups. Ann. Sc. Norm. Super. Pisa Cl. Sci., IV. Ser.11, 327–341 (1984)
Desch, W., Schappacher, W.: Spectral properties of finite-dimensional perturbed linear semigroups. J. Differ. Equations59, 80–102 (1985)
Desch, W., Lasiecka, I., Schappacher, W.: Feedback boundary control problems for linear semigroups. Isr. J. Math.51, 177–207 (1985)
Diekmann, O.: Perturbed dual semigroups and delay equations. To appear in: Infinite dimensional dynamical systems. Proceedings, Lisbon, 1986
Greiner, G.: Perturbing the boundary conditions of a generator. Houston J. Math. (to appear)
Gyllenberg, M.: Stability of a nonlinear age-dependent population model containing a control variable. SIAM J. Appl. Math.43, 1418–1438 (1983)
Hale, J.K.: Theory of functional differential equations. Berlin, Heidelberg, New York: Springer 1977
Heijmans, H.J.A.M.: Dynamics of structured populations. Thesis, Univ. of Amsterdam, 1985
Hille, E., Phillips, R.S.: Functional analysis and semigroups. Providence, R.I.: Am. Math. Soc. 1957
Kappel, F., Schappacher, W.: Non-linear functional differential equations and abstract integral equations. Proc. Roy. Soc. Edinb.84A, 71–91 (1979)
Metz, J.A.J., Diekmann, O. (eds.): Dynamics of physiologically structured populations. Lecture Notes in Biomathematics 68. Berlin, Heidelberg, New York: Springer 1986
Pazy, A.: Semigroups of linear operators and applications to partial differential equations. Berlin, Heidelberg, New York: Springer 1983
Rudin, W.: Real and complex analysis, 2nd ed. New York: McGraw-Hill 1974
Suhadolc, A., Vidav, I.: Linearized Boltzmann equations in spaces of measures. Math. Balk.3, 514–529 (1973)
Thieme, H.R.: Well-posedness of physiologically structured population models for Daphnia magna. Preprint, CWI Report AM-R8609, 1986
Yosida, K.: Functional analysis. Berlin, Heidelberg, New York: Springer 1965
Author information
Authors and Affiliations
Additional information
Supported by ZWO (Netherlands Organization for the Advancement of Pure Research) and DFG (German Research Foundation)
Rights and permissions
About this article
Cite this article
Clément, P., Diekmann, O., Gyllenberg, M. et al. Perturbation theory for dual semigroups. Math. Ann. 277, 709–725 (1987). https://doi.org/10.1007/BF01457866
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01457866