Nonlinear functions and the norm of the propagators of operational equations

abstract

• We explore the relation between nonlinear functions and the norm functions of the propagators of operational equations in infinite-dimensional spaces. A general criterion is obtained to judge whether a given nonlinear function is the norm function of some C 0-semigroup, the propagator of a wellposed Cauchy problem for an operational equation in an infinite-dimensional space, which gives a solution to an open problem posed in Lin et al. (2010) [6]. Moreover, applying our abstract results, we show the existence of two valuable C 0-semigroups, which one has been seeking. 2012 Elsevier B.V.

authors

• Huang, Tingwen

published proceedings

• COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

author list (cited authors)

• Lin, Y. u., Xiao, T., Liang, J., & Huang, T.

citation count

• 1

complete list of authors

• Lin, Yu||Xiao, Ti-Jun||Liang, Jin||Huang, Ting-Wen

publication date

• December 2012

publisher

• Elsevier  Publisher

published in

• Communications in Nonlinear Science and Numerical Simulation  Journal

keywords

• C-0-semigroup
• Growing Logarithmically
• Infinite Dimensional Space
• Non-nilpotent
• Nonlinear Function
• Norm Function
• Propagators

Digital Object Identifier (DOI)

• 10.1016/j.cnsns.2012.04.013

start page

• 4611

end page

• 4615

volume

• 17

issue

• 12

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.cnsns.2012.04.013