Infinitely many radial solutions of a variational problem related to dispersion-managed optical fibers
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- Proc. Amer. Math. Soc. 131 (2003), 2181-2188 Request permission
Abstract:
We consider a non-local variational problem whose critical points are related to bound states in certain optical fibers. The functional is given by $\varphi (u)=\frac {1}{2}|u|^2_{H^1}-\int _0^1\int _{\mathbb {R}^2}|e^{it\Delta }u|^4 dxdt$, and relying on the regularizing properties of the solution $e^{it\Delta }$ to the free Schrödinger equation, it will be shown that $\varphi$ has infinitely many critical points.References
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Additional Information
- Markus Kunze
- Affiliation: FB 6 – Mathematik, Universität Essen, D - 45117 Essen, Germany
- Email: mkunze@ing-math.uni-essen.de
- Received by editor(s): December 13, 2001
- Received by editor(s) in revised form: March 3, 2002
- Published electronically: November 13, 2002
- Communicated by: Andreas Seeger
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2181-2188
- MSC (1991): Primary 35A15, 35Q55; Secondary 78A60
- DOI: https://doi.org/10.1090/S0002-9939-02-06780-1
- MathSciNet review: 1963766