Periodic solutions for partial neutral non densely differential equations

References

• Hale JK. Asymptotic behavior of dissipative systems. Rhode Island: American Mathematical Society; 1988. (Mathematical surveys and monographs; 25).
   Google Scholar
• Hale JK, Sjoerd M, Verduyen L. Introduction to functional differential equations; 1993. (Applied mathematical sciences).
   Google Scholar
• Hale JK. Partial neutral functional differential equations. Rev Roumaine Math Pure Appli. 1994;39:339–344.
   Google Scholar
• Wu J, Xia H. Self-sustained oscillations in a ring array of coupled lossless trans-mission lines. J Differential Equations. 1996;124:247–278. doi: 10.1006/jdeq.1996.0009
   Web of Science ®Google Scholar
• Wu J, Xia H. Rotating waves in neutral partial functional differential equations. J Dynam Differential Equations. 1999;11:209–238. doi: 10.1023/A:1021973228398
   Google Scholar
• Hino Y, Naito T, Minh NV, et al. Almost periodic solutions of differential equations in Banach spaces; 2002. (Stability and control: theory, methods and applications).
   Google Scholar
• Jendoubi C. Unstable manifolds of a class of delayed partial differential equations with nondense domain. Annales Polinicci Mathematici. 2016;118:181–208. doi: 10.4064/ap3913-11-2016
   Web of Science ®Google Scholar
• Jendoubi C. Integral manifolds of a class of delayed partial differential equations with nondense domain. Numer Funct Anal Optim. 2017;38:1024–1044. doi: 10.1080/01630563.2017.1309665
   Web of Science ®Google Scholar
• Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer; 1983.
   Google Scholar
• Wu J. Theory and applications of partial functional differential Equations. New York: Springer; 1996.
   Google Scholar
• Liu JH. Bounded and periodic solutions of differential equations in Banach space. J Appl Math Comput. 1994;65:141–150. doi: 10.1016/0096-3003(94)90171-6
   Web of Science ®Google Scholar
• Liu JH. Bounded and periodic solutions of finite delay evolution equations. Nonlinear Anal. 1998;34:101–111. doi: 10.1016/S0362-546X(97)00606-8
   Web of Science ®Google Scholar
• Webb GF. Theory of nonlinear age-dependent population dynamics. Marcel Dekker; 1985.
   Google Scholar
• Yoshizawa T. Stability theory and the existence of periodic solutions and almost periodic solutions. New York: Springer; 1975. (Applied mathematical sciences; 14).
   Google Scholar
• Burton T. Stability and periodic solutions of ordinary and functional differential equations. Orlando (FL): Academic Press; 1985.
   Google Scholar
• Liu JH, N'Guerekata GM, Minh NV. Topics on stability and periodicity in abstract differential equations. Singapore: World Scientific; 2008. (Series on concrete and applicable mathematics; 6).
   Google Scholar
• Pruss J. Periodic solutions of semilinear evolution equations. Nonlinear Anal. 1979;3:601–612. doi: 10.1016/0362-546X(79)90089-0
   Google Scholar
• Pruss J. Periodic solutions of the thermostat problem. In: Differential equations in Banach spaces. Berlin: Springer; 1986. p. 216–226 (Lecture notes in math.; 1223).
   Google Scholar
• Serrin J. A note on the existence of periodic solutions of the Navier-Stokes equations. Arch Rational Mech Anal. 1959;3:120–122. doi: 10.1007/BF00284169
   Web of Science ®Google Scholar
• Murray JD. Mathematical biology I: an introduction. Berlin: Springer; 2002.
   Google Scholar
• Murray JD. Mathematical biology II: spatial models and biomedical applications. Berlin: Springer; 2003.
   Google Scholar
• Yagi A. Abstract parabolic evolution equations and their applications. Springer; 2009.
   Google Scholar
• Dang NQ, Huy NT. Dichotomy and periodic solutions to partial functional differential equations. Discrete Contin Dyn Syst. 2017;22:3127–3144. doi: 10.3934/dcdsb.2017167
   Web of Science ®Google Scholar
• Rhandi A. Extrapolation methods to solve non-autonomous retarded partial differential equations. Studia Math. 1998;126(3):219–233. doi: 10.4064/sm-126-3-219-233
   Web of Science ®Google Scholar
• Chicone C, Latushkin Y. Evolution semigroups in dynamical systems and differential equations. Providence (RI): American Mathematical Society; 1999. (Mathematical surveys and monographs; 70)
   Google Scholar
• Guhring G, Rabiger F. Asymptotic properties of mild solutions for non-autonomous evolution equations with applications to retarded differential equations. J Abstract Appl Anal. 1999;4:169–194. doi: 10.1155/S1085337599000214
   Google Scholar
• Latushkin Y, Randolph T, Schnaubelt R. Exponential dichotomy and mild solutions of nonautonomous equations in Banach spaces. J Dynam Differential Equations. 1998;10(3):489–510. doi: 10.1023/A:1022609414870
   Google Scholar
• Nagel R, Nickel G. Well posedness for non-autonomous abstract Cauchy problems. Prog Nonlinear Differential Equations Appl. 2002;50:279–239.
   Google Scholar
• Nagel R, Sinestrari E. Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators. In: Functional analysis (Essen, 1991). New York: Dekker; 1994. p. 51–70. (Lecture notes in pure and appl. math.; 150).
   Google Scholar
• Minh NV, Rabiger F, Schnaubelt R. Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half line. Integral Equations Operator Theory. 1998;32:332–353. doi: 10.1007/BF01203774
   Web of Science ®Google Scholar
• Dang NQ, Huy NT. Periodic solutions to evolution equations: existence, conditional stability and admissibility of function spaces. Ann Polon Math. 2016;116:173–195.
   Web of Science ®Google Scholar
• Huy NT. Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line. J Funct Anal. 2006;235:330–354. doi: 10.1016/j.jfa.2005.11.002
   Web of Science ®Google Scholar
• Huy NT. Stable manifolds for semi-linear evolution equations and admissibility of function spaces on a half-line. J Math Anal Appl. 2009;354:372–386. doi: 10.1016/j.jmaa.2008.12.062
   Web of Science ®Google Scholar
• Da Prato G, Sinestrari E. Differential operators with non-dense domain. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze. 1987;14:285–344.
   Google Scholar
• Arendt W, Grabosch A, Greiner G, et al. One-parameter semigroup of positive operators. Berlin: Springer; 1984. (Lecture notes in mathematics; 1184).
   Google Scholar