Delay Differential Equations and Dynamical Systems: Proceedings of a Conference in honor of Kenneth Cooke held in Claremont, California, Jan. 13-16, 1990 (Lecture Notes in Mathematics, 1475)

The Meeting Explored Current Directions Of Research In Delay Differential Equations And Related Dynamical Systems And Celebrated The Contributions Of Kenneth Cooke To This Field On The Occasion Of His 65th Birthday. The Volume Contains Three Survey Papers Reviewing Three Areas Of Current Research And Seventeen Research Contributions. The Research Articles Deal With Qualitative Properties Of Solutions Of Delay Differential Equations And With Bifurcation Problems For Such Equations And Other Dynamical Systems. A Companion Volume In The Biomathematics Series (ln In Biomathematics, Vol. 22) Contains Contributions On Recent Trends In Population And Mathematical Biology. From The Contents: Surveys: K. Cooke, J. Wiener: A Survey Of Differential Equations With Piecewise Continuous Arguments -- J. Hale: Dynamics And Delays -- P. Waltman: A Brief Survey Of Persistence In Dynamical Systems. Research Articles: H. Amann: Hopf Bifurcation In Quasilinear Reaction-diffusion Systems -- L. Carvalho: On The Stability Of Discrete Equations And Ordinary Differential Equations -- G. Conti, P. Nistri, P. Zecca: Sysstems Of Set-valued Equations In Banach Spaces -- J. Franke, H. Stech: Extensions Of An Algorithm For The Analysis Of Nongeneric Hopf Bifurcations, With Applications To Delay-differential Equations -- A. Capieto, J. Mawhin, F. Zanolin: The Coincidence Degree Of Some Functional Differential Operators In Spaces Of Periodic Functions And Related Continuation Theorems -- M. Furi, M.p. Pera: The Forced Spherical Pendulum Does Have Forced Oscillations -- O. Arino: Monotone Semi-flows Which Have A Monotone First Integral -- O. Diekmann, M. Gyllenberg, H.r. Thieme: Semigroups And Renewal Equations On Dual Banach Spaces With Applications To Population Dynamics. S. Busenberg, M. Martelli, Eds. Papers Presented At The International Conference On Differential Equations And Applications To Biology And Population Dynamics. Includes Bibliographical References. A survey of differential equations with piecewise continuous arguments....Pages 1-15 Dynamics and delays....Pages 16-30 A brief survey of persistence in dynamical systems....Pages 31-40 Periodic orbits of planar polynomial Liénard systems with a small parameter....Pages 41-52 Hopf bifurcation in quasilinear reaction-diffusion systems....Pages 53-63 Monotone semi-flows which have a monotone first integral....Pages 64-75 The coincidence degree of some functional differential operators in spaces of periodic functions and related continuation theorems....Pages 76-87 On the stability of discrete equations and ordinary differential equations....Pages 88-97 Systems of set-valued equations in Banach spaces....Pages 98-109 Abstract volterra equations and weak topologies....Pages 110-115 Semigroups and renewal equations on dual Banach spaces with applications to population dynamics....Pages 116-129 Estimates for spatio-temporally dependent reaction diffusion systems....Pages 130-146 The mountain circle theorem....Pages 147-160 Extensions of an algorithm for the analysis of nongeneric Hopf bifurcations, with applications to delay-difference equations....Pages 161-175 The forced spherical pendulum does have forced oscillations....Pages 176-182 Radial bounds for Schrödinger operators in euclidean domains....Pages 183-190 Jumping nonlinearity for 2nd order ODE with positive forcing....Pages 191-203 Moment conditions for a Volterra integral equation in a Banach space....Pages 204-209 Asymptotic behaviors of solutions of a system of linear ordinary differential equations as t →∞....Pages 210-217 Implicit differential equations which are not solvable for the highest derivative....Pages 218-224 A stability analysis for a class of differential-delay equations having time-varying delay....Pages 225-242 On an interval map associated with a delay logistic equation with discontinuous delays....Pages 243-249