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Abstract and Applied Analysis
Volume 1, Issue 4, Pages 351-380
http://dx.doi.org/10.1155/S108533759600019X

Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolution equations

1Department of Mathematics, University of Augsburg, D-86135, Augsburg, Germany
2Department of Mathematics, University of Tübingen, D-72076, Tübingen, Germany

Received 25 July 1996

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [29 citations]

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  • Nv Minh, “On the proof of characterizations of the exponential dichotomy,” Proceedings Of The American Mathematical Society, vol. 127, no. 3, pp. 779–782, 1999. View at Publisher · View at Google Scholar
  • Satoru Murakami, Toshiki Naito, and Nguyen Van Minh, “Evolution Semigroups and Sums of Commuting Operators: A New Approach to the Admissibility Theory of Function Spaces,” Journal of Differential Equations, vol. 164, no. 2, pp. 240–285, 2000. View at Publisher · View at Google Scholar
  • N Van Minh, Js Shin, and T Naito, “New spectral criteria for almost periodic solutions of evolution equations,” Studia Mathematica, vol. 145, no. 2, pp. 97–111, 2001. View at Publisher · View at Google Scholar
  • Tran Thi Loan, and Nguyen Manh Hung, “On the stability of semilinear nonautonomous evolution equations in banach spaces and its application to strongly parabolic equations,” Ukrainian Mathematical Journal, vol. 54, no. 12, pp. 2080–2087, 2002. View at Publisher · View at Google Scholar
  • N Van Minh, and Jh Wu, “Invariant manifolds of partial functional differential equations,” Journal Of Differential Equations, vol. 198, no. 2, pp. 381–421, 2004. View at Publisher · View at Google Scholar
  • Fritz Colonius, Stefan Hilger, Peter Kloeden, and Stefan Siegmund, “Bernd Aulbach—Obituary,” Journal of Difference Equations and Applications, vol. 12, no. 3-4, pp. 237–246, 2006. View at Publisher · View at Google Scholar
  • Nguyen Thieu Huy, “Existence and robustness of exponential dichotomy of linear skew-product semiflows over semiflows,” Journal of Mathematical Analysis and Applications, vol. 333, no. 2, pp. 731–752, 2007. View at Publisher · View at Google Scholar
  • Yutaka Nagabuchi, and Satoru Murakami, “Invariant manifolds for abstract functional differential equations and related Volterra difference equations in a Banach space,” Funkcialaj Ekvacioj-Serio Internacia, vol. 50, no. 1, pp. 133–170, 2007. View at Publisher · View at Google Scholar
  • Amin Boumenir, Nguyen Van Minh, and Vu Kim Tuan, “Frequency modules and nonexistence of quasi-periodic solutions of nonlinear evolution equations,” Semigroup Forum, vol. 76, no. 1, pp. 58–70, 2007. View at Publisher · View at Google Scholar
  • B. Aylaj, M. E. Achhab, and M. Laabissi, “State Trajectories Analysis for a Class of Tubular Reactor Nonlinear Nonautonomous Models,” Abstract and Applied Analysis, vol. 2008, pp. 1–13, 2008. View at Publisher · View at Google Scholar
  • Thieu Huy Nguyen, “Stable manifolds for semi-linear evolution equations and admissibility of function spaces on a half-line,” Journal of Mathematical Analysis and Applications, vol. 354, no. 1, pp. 372–386, 2009. View at Publisher · View at Google Scholar
  • Nguyen Thieu Huy, “Invariant manifolds of admissible classes for semi-linear evolution equations,” Journal of Differential Equations, vol. 246, no. 5, pp. 1820–1844, 2009. View at Publisher · View at Google Scholar
  • Thieu Huy Nguyen, and Phi Ha, “Discretized characterizations of exponential dichotomy of linear skew-product semiflows over semiflows,” Journal of Mathematical Analysis and Applications, vol. 362, no. 1, pp. 46–57, 2010. View at Publisher · View at Google Scholar
  • Thieu Huy Nguyen, “Inertial manifolds for semi-linear parabolic equations in admissible spaces,” Journal of Mathematical Analysis and Applications, vol. 386, no. 2, pp. 894–909, 2012. View at Publisher · View at Google Scholar
  • Nguyen Thieu Huy, Vu Thi Ngoc Ha, and Ha Phi, “Integral manifolds for semilinear evolution equations and admissibility of function spaces,” Ukrainian Mathematical Journal, vol. 64, no. 6, pp. 881–911, 2012. View at Publisher · View at Google Scholar
  • Thieu Huy Nguyen, “Admissibly inertial manifolds for a class of semi-linear evolution equations,” Journal of Differential Equations, vol. 254, no. 6, pp. 2638–2660, 2013. View at Publisher · View at Google Scholar
  • L.Z. Guo, Y.Z. Guo, S.A. Billings, D. Coca, and Z.Q. Lang, “A Volterra series representation for a class of nonlinear infinite dimensional systems with periodic boundary conditions,” Systems & Control Letters, vol. 62, no. 2, pp. 115–123, 2013. View at Publisher · View at Google Scholar
  • Thieu Huy Nguyen, and Trinh Viet Duoc, “Integral manifolds for partial functional differential equations in admissible spaces on a half-line,” Journal of Mathematical Analysis and Applications, 2013. View at Publisher · View at Google Scholar
  • Nguyen Minh, Gaston M. N’guérékata, and Ciprian Preda, “On the asymptotic behavior of the solutions of semilinear nonautonomous equations,” Semigroup Forum, 2013. View at Publisher · View at Google Scholar
  • Thieu Huy Nguyen, and Viet Duoc Trinh, “Unstable Manifolds for Partial Functional Differential Equations in Admissible Spaces on the Whole Line,” Vietnam Journal of Mathematics, 2014. View at Publisher · View at Google Scholar
  • Nt Nguyen Thieu Hu, and Vtn Vu Thi Ngoc Ha, “Admissibly integral manifolds for semilinear evolution equations,” Annales Polonici Mathematici, vol. 112, no. 2, pp. 127–163, 2014. View at Publisher · View at Google Scholar
  • Pham Van Bang, and Nguyen Thieu Huy, “Invariant stable manifolds for partial neutral functional differential equations in admissible spaces on a half-line,” Discrete and Continuous Dynamical Systems - Series B, vol. 20, no. 9, pp. 2993–3011, 2015. View at Publisher · View at Google Scholar
  • Hideaki Matsunaga, Satoru Murakami, Yutaka Nagabuchi, and Nguyen Van Minh, “Center Manifold Theorem and Stability for Integral Equations with Infinite Delay,” Funkcialaj Ekvacioj, vol. 58, no. 1, pp. 87–134, 2015. View at Publisher · View at Google Scholar
  • Thieu Huy Nguyen, and Van Bang Pham, “Unstable Manifolds for Partial Neutral Differential Equations and Admissibility of Function Spaces,” Acta Mathematica Vietnamica, 2016. View at Publisher · View at Google Scholar
  • Ciprian Preda, “A generalisation of a theorem of O. Perron for semilinear evolution equations,” Mathematical Proceedings of the Cambridge Philosophical Society, pp. 1–21, 2016. View at Publisher · View at Google Scholar
  • Chiraz Jendoubi, “Integral manifolds of a class of delayed partial differential equations with nondense domain,” Numerical Functional Analysis and Optimization, 2017. View at Publisher · View at Google Scholar
  • Eric Kokomo, and Yves Emvudu, “Mathematical modeling of the migration’s effect and analysis of the spreading of a cholera epidemic,” Journal of Mathematical Modeling, vol. 6, no. 2, pp. 165–186, 2018. View at Publisher · View at Google Scholar
  • Trinh Viet Duoc, and Nguyen Thieu Huy, “Stable and center-stable manifolds of admissible classes for partial functional differential equations,” Journal of Integral Equations and Applications, vol. 30, no. 4, pp. 543–575, 2018. View at Publisher · View at Google Scholar
  • Hisashi Inaba, “The basic reproduction number $$R_0$$ R 0 in time-heterogeneous environments,” Journal of Mathematical Biology, 2019. View at Publisher · View at Google Scholar