The geometry of the critical set of nonlinear periodic Sturm-Liouville operators

Details The geometry of the critical set of nonlinear periodic Sturm-Liouville operators The geometry of the critical set of nonlinear periodic Sturm-Liouville operators

2007-07-09

arxiv.org/abs/0707.1256v2

J. Differential Equations246(2009) 3380-3397

Mathematics

Functional Analysis

Added references, fixed typos; 24 pages, 4 figures

Scientific paper

10.1016/j.jde.2008.10.021

We study the critical set C of the nonlinear differential operator F(u) = -u" + f(u) defined on a Sobolev space of periodic functions H^p(S^1), p >= 1. Let R^2_{xy} \subset R^3 be the plane z = 0 and, for n > 0, let cone_n be the cone x^2 + y^2 = tan^2 z, |z - 2 pi n| < pi/2; also set Sigma = R^2_{xy} U U_{n > 0} cone_n. For a generic smooth nonlinearity f: R -> R with surjective derivative, we show that there is a diffeomorphism between the pairs (H^p(S^1), C) and (R^3, Sigma) x H where H is a real separable infinite dimensional Hilbert space.

Affiliated with

Also associated with

No associations

Rating

The geometry of the critical set of nonlinear periodic Sturm-Liouville operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The geometry of the critical set of nonlinear periodic Sturm-Liouville operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The geometry of the critical set of nonlinear periodic Sturm-Liouville operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-159253