On (h, k)-Decay of Evolution Operators in Banach Spaces
[1]
Guo-Liang Lei, School of Science, Hubei University of Automotive Technology, Shiyan, Hubei 442002, China.
[2]
Tian Yue, School of Science, Hubei University of Automotive Technology, Shiyan, Hubei 442002, China.
The main aim of this work is to define and exemplify various decay concepts and to emphasize connections between them. These decay concepts are included in a general concept,the so-called (h, k)-decay. Some illustrating examples clarify the relations between these properties.
Evolution Operator, (h, k)-Decay, Exponential Decay, Polynomial Decay
[1]
L. Barreira and C. Valls, Stability of Nonautonomous Differential Equations, Lecture Notes in Math. 1926, Springer, 2008.
[2]
L. Barreira and C. Valls, Polynomial growth rates, Nonlinear Anal. 71 (2009), no. 11, 5208--5219.
[3]
J.L. Fenner and M. Pinto, On (h, k) manifolds with asymptotic phase, J. Math. Anal. Appl. 216(1997), 549--568.
[4]
M. Megan, T. Ceausu and A. A. Minda, On Barreira-Valls polynomial stability of evolution operators in Banach spaces, Electron. J. Qual. Theo. Differ. Equat. (2011), no. 33, 1--10.
[5]
M. Megan, T. Ceausu and A. A. Minda, On polynomial stability of variational nonautonomous difference equations in Banach spaces, Int. J. Anal. 2013 (2013), Article ID 407958, 1--7.
[6]
M. Megan, T. Ceausu and M. L. Ramneantu, Polynomial stability of evolution operators in Banach spaces, Opuscula Math. 31 (2011), no. 2, 279--288.
[7]
M. Megan, On (h, k)-dichotomy of evolution operators in Banach spaces, Dynam. Syst. Appl. 5 (1996), 189--196.
[8]
A.A. Minda and M. Megan, On (h, k)-exponential stability of evolution operators in Banach spaces, J. Adv. Math. Stud. 3 (2010), 1--4.
[9]
A.A. Minda and M. Megan, On (h, k)-stability of evolution operators in Banach spaces, Appl. Math. Lett. 24 (2011), 44--48.
[10]
A.A. Minda, On (h, k)-growth of evolution operators in Banach spaces, Acta Univ. Apulensis 26 (2011), 197--202.
[11]
R.Naulin and M. Pinto, Dichotomies and asymptotic solutions of nonlinear differential systems, Nonlinear Anal. TMA 23(1994), 871--882.
[12]
M. Pinto, Asymptotic integrations of systems resulting from the perturbation of an h-system, J. Math. Anal. Appl. 131 (1988), 194--216.
[13]
M. Pinto, Dichotomies and asymptotic formulae of solutions of differential equations, J. Math. Anal. Appl. 195 (1995), 16--31.
[14]
X.-Q. Song, T. Yue and D.-Q. Li, Nonuniform exponential trichotomy for linear discrete-time systems in Banach spaces, J. Funct. Space Appl. 2013 (2013), Article ID 645250, 1--6.
[15]
T. Yue, X.-Q. Song and D.-Q. Li, On weak exponential expansineness of evolution families in Banach spaces, The Scientific World J. 2013 (2013), Article ID 284630, 1--6.
[16]
T. Yue, X.-Q. Song and D.-Q. Li, On weak exponential expansineness of skew-evolution semiflows in Banach spaces, J. Inequal. Appl. 2014 (2014), Article 165, 1--11.