Periodic solutions of nonlinear abstract differential equations with infinite delay

1 Amann, H. Periodic solutions of semilinear parabolic equations Nonlinear Analysis (Edited by L. Cesari, R. Kannan and H. F. Weinberger), Academic press, New York 1978 1-29 MR0499089

2 Arino, O. A.; Burton, T. A.; Haddock, J. R. Periodic solutions to functional-differential equations Proc. Roy. Soc. Edinburgh Sect. A. 101A 1985 253-271 MR0824225

3 Burton, T. A. Volterra Integral and Differential Equations Academic Press, New York 1983 MR0715428 Cache/Bu/Burton,DiJferential,*,1983,1984 4 Burton, T. A. Stability and Periodic Solutions of Ordinary and Functional Differential Equations Academic Press, Orlando, Florida 1985 MR0837654 88 Cache/Bu/Burton,Functional,*,1985,1986 x+337 5 Burton, T. A., The nonlinear wave equation as a Liénard equation, Funkcial. Ekvac, to appear MR1150878 1150878

6 Burton, T. A.; Eloe, P. W.; Islam, M. N. Periodic solutions of linear integro-differential equations Math. Nachrichten 147 1990 175-184 MR1127322 Cache/Bu/Burton,integrodifferential,Math*,1990,1991

7 Burton, T. A.; Eloe, P. W.; Islam, M. N., Nonlinear integrodifferential equations and a priori bounds on periodic solutions, Ann. Mat. Pura Appl., to appear MR1174820

8 Burton, T. A.; Zhang, B. Uniform ultimate boundedness and periodicity in functional differential equations Tohoku Math. J. 42 1990 93-100 MR1036476 Cache/Bu/Burton,boundedness,T\^ohoku*,1990,1991

9 Burton, T. A.; Zhang, B. Periodic solutions of abstract differential equations with infinite delay J. Differential equations 90 1991 357-396 MR1101245 100 Cache/Bu/Burton,solutions,J*,1991,1992

10 Cesari, L.; Kannan, R. Solutions of nonlinear hyperbolic equations at resonance Nonlinear Anal. 6 1982 751-805 MR0671720 100 Cache/Ce/Cesari,hyperbolic,Nonlinear*,1982,1983

11 Cesari, L.; Kannan, R. Periodic solutions of nonlinear wave equations with damping Rend. Circ. Mat. Palermo 31 1982 421-432 MR0693588 100 Cache/Ce/Cesari,solutions,Rend*,1982,1983

12 Cesari, L.; Kannan, R. Solutions of nonlinear wave equations with nonlinear damping Comm. Partial Diff. Equation 8 1983 199-211 MR0692283 100 Cache/Ce/Cesari,Solutions,Comm*,1983,1984

13 DaPrato, G. Maximal regularity for abstract differential equations and applications to the existence of periodic solutions Trends in the Theory and Practice of Nonlinear Analysis (Edited by V. Lakshmikantham), North-Holland, Amsterdam 1985 121-126 MR0817480

14 DaPrato, G.; Lunardi, A. Periodic solutions for linear integro-differential equations with infinite delay in Banach space Differential Equations in Banach space (Edited by A. Favini and E. Obrent), Springer, New York 1986 49-60 MR0872516

15 Dieudonné, J. A. Foundations of Modern Analysis Academic press, New York-London 1960 MR0120319 100 Cache/Di/Dieudonné,Foundations,*,1960,1961 xiv+361 16 Dugundji, J.; Granas, A. Fixed Point Theory Warszawa 1982 MR0660439 100 Cache/Du/Dugundji,Theory,*,1982,1983 209

17 Fitzgibbon, W. E. Strongly damped quasilinear evolution equations J. Math. Anal. Appl. 79 1981 536-550 MR0606499 100 Cache/Fi/Fitzgibbon,quasilinear,J*,1981,1982

18 Friedman, A. Partial Differential Equations Krieger Pub. Co., Huntington-New York 1976 MR0454266 100 Cache/Fr/Friedman,Partial,*,1976,1977 i+262

19 Fucik, S.; Mawhin, J. Generalized periodic solutions of nonlinear telegraph equations Nonlinear Anal. 2 1978 609-617 MR0512156 100 Cache/Fu/Fucik,Generalized,Nonlinear*,1978,1979

20 Granas, A. Sur la méthode de continuite de Poincaré C. R. Acad. Sci. Paris 282 1976 983-985 MR0407894 100 Cache/Gr/Granas,continuite,C*,1976,1977

21 Greenberg, J.; MacCamy, R.; Mizel, V. On the existence, uniqueness, and stability of solutions of the equation $\sigma'(u_x)u_{xx}+\lambda u_{xtx}=\rho u_{tt}$ J. Math. Mech. 17 1967/1968 707-728 MR0225026 75 Cache/Gr/Greenberg,uniqueness,,J*,1968,1969

22 Hale, J. K. Theory of Functional Differential Equations Springer, New York 1977 MR0508721 100 Cache/Ha/Hale,Functional,*,1977,1978 x+365 23 Hale, J. K. Asymptotic Behavior of Dissipative Systems Amer. Math. Soc., Providence, R. I. 1988 MR0941371 100 Cache/Ha/Hale,Dissipative,*,1988,1989 x+198 24 Henry, D. Geometric Theory of Semilinear Parabolic Equations Lecture Notes in Math., 840, Springer, New York 1981 MR0610244 100 Cache/He/Henry,Semilinear,*,1981,1982 iv+348

25 Kannan, R.; Lakshmikantham, V. Periodic solutions of nonlinear hyperbolic problems Comp. Math. Appl. 9 1983 479-486 MR0702666 100 Cache/Ka/Kannan,hyperbolic,Comp*,1983,1984

26 Massatt, P. Limiting behavior for strongly damped nonlinear wave equations J. Differential equations 48 1983 334-349 MR0702424 100 Cache/Ma/Massatt,nonlinear,J*,1983,1984

27 Mawhin, J. Periodic solutions of nonlinear telegraph equations Dynamic Systems (Edited by A. R. Bednacek and L. Cesari) 1976 193-210 MR0460914

28 Nachlinger, P. R.; Nunzato, J. W. Stability of uniform temperature fields in linear heat conductions with memory Int. J. Engng. Sci. 14 1976 693-701 MR0459158 90 Cache/Na/Nachlinger,temperature,Int*,1976,1977

29 Nakao, M. On boundedness, periodicity and almost periodicity of solutions of some nonlinear parabolic equations J. Differential Equations 19 1975 371-385 MR0390456 92 Cache/Na/Nakao,boundedness,,J*,1975,1976

30 Nakao, M. Bounded, periodic or almost periodic solutions of nonlinear hyperbolic partial differential equations J. Differential Equations 23 1977 368-386 MR0470428 90 Cache/Na/Nakao,hyperbolic,J*,1977,1978

31 Nakao, M. Bounded, periodic and almost periodic classical solution of some nonlinear wave equations with a dissipative term J. Math. Soc. Japan 30 1978 375-394 MR0492914 93 Cache/Na/Nakao,dissipative,J*,1978,1979

32 Nakao, M. Periodic solutions and decay for some nonlinear wave equations with sublinear dissipative terms Nonlinear anal. 10 1986 587-602 MR0844988 100 Cache/Na/Nakao,dissipative,Nonlinear*,1986,1987

33 Niikura, Y.; Yamada, Y. Bifurcation of periodic solutions for nonlinear parabolic equations with infinite delays Funkcial. Ekvac. 29 1986 309-333 MR0904545 0904545 100 Cache/Ni/Niikura,Bifurcation,Funkcial*,1986,1987 34 Pazy, A. Semigroups of Linear Operators and Applications to Partial Differential Equations Springer, New York 1983 MR0710486 100 Cache/Pa/Pazy,Applications,*,1983,1984 viii+279 35 Walker, J. A. Dynamical Systems and Evolution Equations Plenum, New York 1980 MR0561511 100 Cache/Wa/Walker,Dynamical,*,1980,1981 viii+236

36 Webb, G. Existence and asymptotic behavior for a strongly damped nonlinear wave equation Can. J. Math. 32 1980 631-643 MR0586981 100 Cache/We/Webb,asymptotic,Can*,1980,1981

37 Yoshizawa, T. Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions Springer, New York 1975 MR0466797 100 Cache/Yo/Yoshizawa,Stability,*,1975,1976 vii+233