Functional differential equations of mixed type: The linear autonomous case

Springer Science and Business Media LLC - Tập 1 - Trang 121-143 - 1989
Aldo Rustichini1
1AT&T Bell Laboratories, Murray Hill

Tóm tắt

Functional differential equations of mixed type (MFDE) are introduced; in these equations of functional type, the time derivative may depend both on past and future values of the variables. Here the linear autonomous case is considered. We study the spectrum of the (unbounded) operator, and construct continuous semigroups on the stable, center, and unstable subspaces.

Tài liệu tham khảo

Banks, H. T., and Manitius, A. (1975).Projection series for retarded functional differential equations with application to optimal control problems.J. Differential Equations 18, 296–332. Bellman, R., and Cooke, K. (1963).Differential Difference Equations, Academic Press, New York. Chi, H. Bell, J., and Hassard, B. (1986).Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory.J. Math. Biol. 24, 583–601. Hale, J. (1977).Theory of Functional Differential Equations, Springer-Verlag, New York. Hale, J. (1979).Nonlinear oscillations in equations with delays. InNonlinear Oscillations in Biology (Lectures in Applied Mathematics, vol. 17), American Mathematical Society, Providence, 157–185. Hille, E., and Phillips, R. (1957).Functional Analysis and Semigroups, American Mathematical Society Colleg. Publ., vol. 31, Providence, Rhode Island. Pontryagin, L. S., Gamkreledze, R. V., and Mischenko, E. F. (1962).The Mathematical Theory of Optimal Processes, Interscience, New York. Rustichini, A. (1989). Hopf bifurcation for functional differential equations of mixed type.J. Dynamics and Differential Equations 1, 145–177.