The geometry of the critical set of nonlinear periodic Sturm-Liouville operators |
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Authors: | Dan Burghelea Carlos Tomei |
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Affiliation: | a Department of Mathematics, Ohio State University, 231 West 18th Ave, Columbus, OH 43210-1174, USA b Departamento de Matemática, PUC-Rio, R. Marquês de S. Vicente 225, Rio de Janeiro, RJ 22453-900, Brazil |
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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 n 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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Keywords: | 34B15 34B24 46T05 |
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