On the structure of
the global attractor for non-autonomous dynamical systems with weak convergence
Pages: 809 - 828,
Issue 2,
March 2012
doi:10.3934/cpaa.2012.11.809 Abstract
References
Full text (495.9K)
Related Articles
Tomás Caraballo - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla, Spain (email)
David Cheban - State University of Moldova, Department of Mathematics and Informatics, A. Mateevich Street 60, MD–2009 Chişinău, Moldavia (email)
| 1 |
N. P. Bhatia and G. P. Szegö, "Stability Theory of Dynamical Systems," Lecture Notes in Mathematics, Springer, Berlin-Heidelberg-New York, 1970. |
|
| 2 |
I. U. Bronsteyn, "Extensions of Minimal Transformation Group," Noordhoff, 1979. |
|
| 3 |
B. F. Bylov, R. E. Vinograd, D. M. Grobman and V. V. Nemytskii, "Lyapunov Exponents Theory and Its Applications to Problems of Stabity," Moscow, Nauka, 1966, 576 pp. (in Russian). |
|
| 4 |
T. Caraballo and D. N. Cheban, Levitan/Bohr almost periodic and almost automorphic solutions of second-order monotone differential equations, J. Differ. Eqns., 251 (2011), 708-727. |
|
| 5 |
D. N. Cheban, Quasiperiodic solutions of the dissipative systems with quasiperiodic coefficients, Differential Equations, 22 (1986), 267-278. |
|
| 6 |
D. N. Cheban, $\mathbb C$-analytic dissipative dynamical systems, Differential Equations, 22 (1986), 1915-1922. |
|
| 7 |
D. N. Cheban, Boundedness, dissipativity and almost periodicity of the solutions of linear and weakly nonlinear systems of differential equations, Dynamical systems and boundary value problems, Kishinev, "Shtiintsa," (1987), 143-159. |
|
| 8 |
D. N. Cheban, Global pullback atttactors of C-analytic nonautonomous dynamical systems, Stochastics and Dynamics, 1 (2001), 511-535. |
|
| 9 |
D. N. Cheban, "Global Attractors of Non-Autonomous Dissipative Dynamical Systems," Interdisciplinary Mathematical Sciences 1. River Edge, NJ: World Scientific, 2004, 528pp. |
|
| 10 |
D. N. Cheban, Levitan almost periodic and almost automorphic solutions of $V$-monotone differential equations, J. Dynamics and Differential Equations, 20 (2008), 669-697. |
|
| 11 |
D. N. Cheban, "Asymptotically Almost Periodic Solutions of Differential Equations," Hindawi Publishing Corporation, New York, 2009, 203 pp. |
|
| 12 |
D. N. Cheban, "Global Attractors of Set-Valued Dynamical and Control Systems," Nova Science Publishers, New York, 2010. |
|
| 13 |
D. N. Cheban and C. Mammana, Invariant manifolds, global attractors and almost periodic solutions of non-autonomous difference equations, Nonlinear Analysis TMA, 56 (2004), 465-484. |
|
| 14 |
D. N. Cheban and B. Schmalfuß, Invariant manifolds, global attractors, almost automorphic and almost periodic solutions of non-autonomous differential equations, J. Math. Anal. Appl., 340 (2008), 374-393. |
|
| 15 |
C. Conley, "Isolated Invariant Sets and the Morse Index," Region. Conf. Ser. Math., No.38, 1978. Am. Math. Soc., Providence, RI. |
|
| 16 |
B. P. Demidovich, On Dissipativity of Certain Nonlinear Systems of Differential Equations, I, Vestnik MGU, 6 (1961), 19-27. |
|
| 17 |
B. P. Demidovich, On Dissipativity of Certain Nonlinear Systems of Differential Equations, II, Vestnik MGU, 1 (1962), 3-8. |
|
| 18 |
B. P. Demidovich, "Lectures on Mathematical Theory of Stability," Moscow, Nauka, 1967. (in Russian) |
|
| 19 |
A. M. Fink and P. O. Fredericson, Ultimate boundedness does not imply almost periodicity, Journal of Differential Equations, 9 (1971), 280-284. |
|
| 20 |
J. K. Hale, "Asymptotic Behaviour of Dissipative Systems," Amer. Math. Soc., Providence, RI, 1988. |
|
| 21 |
M. W. Hirsch, H. L. Smith and X.-Q. Zhao, Chain transitivity, attractivity, and strong repellers for semidynamical systems, J. Dyn. Diff. Eqns, 13 (2001), 107-131. |
|
| 22 |
B. M. Levitan and V. V. Zhikov, "Almost Periodic Functions and Differential Equations," Cambridge Univ. Press, London, 1982. |
|
| 23 |
A. Pavlov, A. Pogrowsky, N. van de Wouw and N. Nijmeijer, Convergent dynamics, a tribute to Boris Pavlovich Demidovich, Systems and Control Letters, 52 (2007), 257-261. |
|
| 24 |
V. A. Pliss, "Nonlocal Problems in the Theory of Oscillations," Nauka, Moscow, 1964 (in Russian). [English translation: Nonlocal Problems in the Theory of Oscillations, Academic Press, 1966.] |
|
| 25 |
V. A. Pliss, "Integral Sets of Periodic Systems of Differential Equations," Nauka, Moscow, 1977 (in Russian). |
|
| 26 |
G. R. Sell, "Topological Dynamics and Ordinary Differential Equations," Van Nostrand-Reinhold, London, 1971. |
|
| 27 |
B. A. Shcherbakov, The comparability of the motions of dynamical systems with regard to the nature of their recurrence, Differential Equations, 11 (1975), 1246-1255. |
|
| 28 |
B. A. Shcherbakov, "Poisson Stability of Motions of Dynamical Systems and Solutions of Differential Equations," Ştiinţa, Chişinău, 1985. (In Russian) |
|
| 29 |
R. E. Vinograd, Inapplicability of the method of characteristic exponents to the study of non-linear differential equations, Mat. Sb. N.S., 41 (1957), 431-438. (in Russian) |
|
| 30 |
T. Yoshizawa, "Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions," Applied Mathematical Sciences, Vol. 14, Springer-Verlag, New York-Heidelberg, 1975. vii+233 pp. |
|
| 31 |
V. V. Zhikov, On stability and unstability of Levinson's centre, Differentsial'nye Uravneniya, 8 (1972), 2167-2170. |
|
| 32 |
V. V. Zhikov, Monotonicity in the theory of almost periodic solutions of non-linear operator equations, Mat. Sbornik, 90 (1973), 214-228; English transl., Math. USSR-Sb., 19 (1974), 209-223. |
|
| 33 |
V. I. Zubov, "The Methods of A. M. Lyapunov and Their Application," Noordhoof, Groningen, 1964. |
|
| 34 |
V. I. Zubov, "Theory of Oscillations," Nauka, Moscow, 1979. (in Russian) |
|
Go to top
|