Periodic solutions of difference-differential equations

SummaryThe existence theorem of R. Nussbaum for periodic solutions of difference-differential equations is generalized to equations with a damping term. The study of such equations is motivated by recent theories of neural interactions in certain compound eyes.

[1]  Shui-Nee Chow,et al.  Existence of periodic solutions of autonomous functional differential equations , 1974 .

[2]  B. D. Coleman Consequences of delayed lateral inhibition in the retina of Limulus. I. Elementary theory of spatially uniform fields. , 1975, Journal of theoretical biology.

[3]  H. Walther Existence of a non-constant periodic solution of a non-linear autonomous functional differential equation representing the growth of a single species population , 1975, Journal of mathematical biology.

[4]  F. Browder A new generalization of the Schauder fixed point theorem , 1967 .

[5]  B. D. Coleman,et al.  Theory of the response of the limulus retina to periodic excitation , 1976, Journal of Mathematical Biology.

[6]  B. D. Coleman Consequences of delayed lateral inhibition in the retina of Limulus. II. Theory of spatially uniform fields, assuming the four-point property. , 1975, Journal of Theoretical Biology.

[7]  G.Stephen Jones,et al.  The existence of periodic solutions of f′(x) = − αf(x − 1){1 + f(x)} , 1962 .

[8]  R. B. Grafton,et al.  A periodicity theorem for autonomous functional differential equations , 1969 .

[9]  B. D. Coleman,et al.  Periodic Solutions of Certain Nonlinear Integral Equations with a Time Lag , 1976 .

[10]  Roger D. Nussbaum,et al.  Periodic solutions of some nonlinear autonomous functional differential equations , 1974 .

[11]  B. D. Coleman,et al.  Theory of delayed lateral inhibition in the compound eye of limulus. , 1974, Proceedings of the National Academy of Sciences of the United States of America.