Nonlinear functions and the norm of the propagators of operational equations

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 12, 2012, Pages 4611-4615

  Lin, Yu ^a   Xiao, Ti Jun ^b   Liang, Jin ^c   Huang, Ting Wen ^d  

^a HONGHE UNIVERSITY   (China)

^b FUDAN UNIVERSITY   (China)

^c SHANGHAI JIAO TONG UNIVERSITY   (China)

^d TEXAS A AND M UNIVERSITY AT QATAR   (Qatar)

Author keywords

Growing logarithmically; Infinite dimensional space; Non nilpotent; Nonlinear function; Norm function; Propagators

Indexed keywords

INTEGRAL EQUATIONS; NONLINEAR EQUATIONS;

DIMENSIONAL SPACES; GROWING LOGARITHMICALLY; INFINITE DIMENSIONAL; INFINITE DIMENSIONAL SPACE; NILPOTENT; NON-NILPOTENT; NONLINEAR FUNCTIONS; NORM FUNCTION; OPERATIONAL EQUATIONS; PROPAGATOR;

FUNCTIONS;

EID: 84864417868     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2012.04.013     Document Type: Article

References (10)

1. Borwein J.M., Lewis A.S. Convex analysis and nonlinear optimization: theory and examples 2000, Springer, New York.
2. Engel K.J., Nagel R. One-parameter semigroups for linear evolution equations. GTM 2000, vol. 194. Springer-Verlag, New York.
3. Fattorini H.O. The cauchy problem. Encyclopedia of mathematics and its applications 1983, vol.18. Addison-Wesley, Reading, MA.
4. Fattorini H.O. Second order linear differential equations in Banach spaces. North-Holland mathematical studies 1985, vol. 108. North-Holland Publishing Co., Amsterdam.
5. Goldstein J.A. Semigroups of linear operators and applications. Oxford mathematical monographs 1985, Oxford Univ. Press, New York.
6. Lin Y., Xiao T.J., Liang J. Notes on the propagators of evolution equations. Adv Differ Equ 2010, 8. Art. ID 795484.
7. Liu James H., Nguérékata G.M., Minh N.V. Topics on stability and periodicity in abstract differential equations. Series on concrete and applicable mathematics 2008, vol. 6. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ.
8. Pazy A. Semigroups of linear operators and applications to partial differential equations. Appl Math Sci 1983, vol. 44. Springer-Verlag, New York.
9. van Casteren J. Generators of strongly continuous semigroups. Research notes in mathematics 1985, Pitman Publishing Limited, London.
10. Xiao T.J., Liang J. The Cauchy problem for higher-order abstract differential equations. Lecture notes in mathematics 1998, vol. 1701. Springer, Berlin, New York.