Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4611950 | Journal of Differential Equations | 2009 | 18 Pages |
Abstract
We study the critical set C of the nonlinear differential operator F(u)=−u″+f(u) defined on a Sobolev space of periodic functions Hp(S1), p⩾1. Let be the plane z=0 and, for n>0, let be the cone x2+y2=tan2z, |z−2πn|<π/2; also set . For a generic smooth nonlinearity f:R→R with surjective derivative, we show that there is a diffeomorphism between the pairs (Hp(S1),C) and (R3,Σ)×H where H is a real separable infinite-dimensional Hilbert space.
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