Discrete and continuous versions of Barbashin-type theorem of linear skew-evolution semiflows

References

• Perron , O . 1930 . Die stabilitatsfrage bei differentialgleichungen . Math. Z. , 32 : 703 – 728 .
   Google Scholar
• Minh , NV , Räbiger , FR and Schnaubelt , R . 1998 . Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line . Integral Equ. Oper. Theory , 32 : 332 – 353 .
   Web of Science ®Google Scholar
• Huy , NT and Minh , NV . 2001 . Exponential Dichotomy of Difference Equations and Applications to Evolution Equations on the Half-Line . Comp. Math. Appl. , 42 : 301 – 311 .
   Web of Science ®Google Scholar
• Latushkin , Y and Schnaubelt , R . 1999 . Evolution semigroups, translation algebras and exponential dichotomy of cocycles . J. Diff. Equ. , 159 : 321 – 369 .
   Google Scholar
• Ta , L . 1934 . Die Stabilitäts frage bei Differenzeng lei chungen . Acta Math. , 63 : 99 – 141 .
   Google Scholar
• Halanay , A and Wexler , D . 1968 . Teoria calitativa a sistemelor cu impulsuri , Bucuresti : Editura Academiei .
   Google Scholar
• Daleckii , JL and Krein , MG . 1974 . “ Stability of Solution of Differential Equations in Banach spaces ” . In American Mathematical Society , RI : Providence .
   Google Scholar
• Massera , JL and Schffer , JJ . 1966 . Linear Differential Equations and Function Spaces , New York : Academic Press .
   Google Scholar
• B. Aulbach and N.V. Minh, Semigroups and exponential stability of nonautonomous linear differential equations on the half-line, in Dynamical Systems and Applications, World Scientific Series in Applicable Analysis 4, R.P. Agarwal ed., World Scientific Publishing Co., Inc., New Jersey, 1995, pp. 45–61.
   Google Scholar
• Henry , D . 1981 . Geometric Theory of Semilinear Parabolic Equations , New York : Springer-Verlag .
   Google Scholar
• Novo , S and Obaya , R . 2004 . Strictly ordered minimal subsets of a class of convex monotone skew-product semiflows . J. Diff. Equ. , 196 : 249 – 288 .
   Google Scholar
• Preda , P , Pogan , A and Preda , C . 2006 . Functionals on function and sequence spaces connected with the exponential stability of evolutionary processes . Czech. Math. J. , 56 : 425 – 435 .
   Google Scholar
• Rolewicz , S . 1986 . On uniform N-equistability . J. Math. Anal. Appl. , 115 : 434 – 441 .
   Web of Science ®Google Scholar
• Datko , R . 1973 . Uniform asymtotic stability of evolutionary processes in Banach spaces . SIAM J. Math. Anal. , 3 : 428 – 445 .
   Google Scholar
• Datko , R . 1970 . Extending a theorem of Lyapunov to Hilbert spaces . J. Math. Anal. Appl. , 32 : 610 – 616 .
   Google Scholar
• Zabczyk , J . 1971 . Remarks on the control of discrete-time distributed parameter systems . SIAM J. Control Optim. , 12 : 721 – 735 .
   Google Scholar
• Pazy , A . 1983 . Semigroups of Linear Operators and Applications to Partial Differnetial Equations , Berlin : Springer .
   Google Scholar
• Hai , PV . 2010 . Continuous and discrete characterizations for the uniform exponential stability of linear skew-evolution semiflows . Nonlinear Anal. Theory Appl. , 72 : 4390 – 4396 .
   Web of Science ®Google Scholar
• Hai , PV . 2010 . Some results about uniform exponential stability of linear skew-evolution semiflows . Int. J. Evol. Equ. , 4 : 27 – 40 .
   Google Scholar
• Megan , M and Pogan , A . 2003 . On exponential h-expansiveness of semigroups of operators in Banach spaces . Nonlinear Anal. Theory Appl. , 52 : 545 – 556 .
   Google Scholar
• Megan , M , Sasu , AL and Sasu , B . 2002 . On uniform exponential stability of linear skew-product semiflows in Banach spaces . Bull. Belg. Math. Soc. – Simon Stevin , 9 : 143 – 154 .
   Web of Science ®Google Scholar
• Van Neerven , JMAM . 1996 . “ The Asymptotic Behaviour of Semigroups of Linear Operators ” . In Theory, Advances and Applications , Vol. 88 , Boston : Birkhauser .
   Google Scholar
• Van Neerven , JMAM . 1995 . Exponential stability of operators and semigroups . J. Funct. Anal. , 130 : 293 – 309 .
   Web of Science ®Google Scholar
• Barbashin , EA . 1967 . Introduction in the theory of Stability , Moscow : Izd. Nauka .
   Google Scholar
• Stoica , C and Megan , M . 2010 . On uniform exponential stability for skew-evolution semiflows on Banach spaces . Nonlinear Anal. Theory Appl. , 72 : 1305 – 1313 .
   Google Scholar