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Minimal periods of semilinear evolution equations with Lipschitz nonlinearity revisited
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Robinson, James C. and Vidal-López, Alejandro (2013) Minimal periods of semilinear evolution equations with Lipschitz nonlinearity revisited. Journal of Differential Equations, Volume 254 (Number 11). pp. 4279-4289. doi:10.1016/j.jde.2013.03.001 ISSN 0022-0396.
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Official URL: http://dx.doi.org/10.1016/j.jde.2013.03.001
Abstract
We show that when A is a self-adjoint sectorial operator on a Hilbert space, for 0 <= alpha <= 1 there exists a constant K alpha, depending only on a, such that if f :D(A(alpha)))- X satisfies parallel to f (u) - f (v)parallel to(x) <= L parallel to A(alpha) (u - v)parallel to(x) then any periodic orbit of the equation u = -Au f(u) has period at least K alpha L-1/(1-alpha). This generalises our previous result [J.C. Robinson, A. Vidal-Lopez, Minimal periods of semilinear evolution equations with Lipschitz nonlinearity, J. Differential Equations 220 (2006) 396-406] which was restricted to 0 <= alpha <= 1/2 and A(-1) compact.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Differential Equations | ||||
Publisher: | Academic Press | ||||
ISSN: | 0022-0396 | ||||
Official Date: | 1 June 2013 | ||||
Dates: |
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Volume: | Volume 254 | ||||
Number: | Number 11 | ||||
Page Range: | pp. 4279-4289 | ||||
DOI: | 10.1016/j.jde.2013.03.001 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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