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Title of Journal: Math Ann

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Abbravation: Mathematische Annalen

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Springer-Verlag

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DOI

10.1016/0161-5890(95)00063-1

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1432-1807

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Configuration spaces transfer and 2nodal soluti

Authors: Thomas Bartsch Mónica Clapp Tobias Weth
Publish Date: 2007/01/10
Volume: 338, Issue: 1, Pages: 147-185
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Abstract

We establish new lower bounds for the number of nodal bound states for the semiclassical nonlinear Schrödinger equation varepsilon2 Delta u+ axu=up2u with bounded and uniformly continuous potential a The solutions we obtain have precisely two nodal domains and their positive and negative parts concentrate near the set of minimum points of a Our approach is independent of penalization techniques and yields in some cases the existence of infinitely many nodal solutions for fixed varepsilon Via a dynamical systems approach we exhibit positively invariant sets of sign changing functions for the negative gradient flow of the associated energy functional We analyze these sets on the cohomology level with the help of Dold’s fixed point transfer In particular we estimate their cuplength in terms of the cuplength of equivariant configuration spaces of subsets of mathbbRN We also provide new estimates of the cuplength of configuration spacesAlbrecht Dold und Dieter Puppe gewidmet Diese im Jahr 2004 entstandene Arbeit war ursprünglich dem 50 Doktorjubiläum von Albrecht Dold und Dieter Puppe gewidmet Beide promovierten im Jahr 1954 an der Universität Heidelberg bei Herbert Seifert TB und MC verdanken ihnen sehr viel

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  1. Estimates of the Green function for X-elliptic operators
  2. Fibred multilinks and singularities $${f \overline g}$$
  3. The NSLUC property and Klee envelope
  4. Hölder estimates for parabolic p ( x , t )-Laplacian systems
  5. Ricci flow on surfaces with cusps
  6. A non-laminar dynamical Green current
  7. Artin characters, Hurwitz trees and the lifting problem
  8. Generic non-selfadjoint Zakharov–Shabat operators
  9. Strichartz estimates via the Schrödinger maximal operator
  10. Examples of relative deformation spaces that are not locally connected
  11. Polynomial approximation of Berkovich spaces and definable types
  12. Prographes sylvestres et groupes profinis presque libres
  13. Zone diagrams in Euclidean spaces and in other normed spaces
  14. A critical radius for unit Hopf vector fields on spheres
  15. Many triangulated 3-spheres
  16. New examples of c 0 -saturated Banach spaces
  17. Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle
  18. Relatively weakly open sets in closed balls of Banach spaces, and real JB * -triples of finite rank
  19. The Bergman metric on complete Kähler manifolds
  20. Conformal dimension via subcomplexes for small cancellation and random groups
  21. Analytic torsion of Hirzebruch surfaces
  22. Déformations des cônes de vecteurs primitifs
  23. Radial entire solutions for supercritical biharmonic equations
  24. Weighted Calderón–Zygmund and Rellich inequalities in $$L^p$$
  25. On entropy, regularity and rigidity for convex representations of hyperbolic manifolds
  26. Rigidity of proper holomorphic maps between bounded symmetric domains
  27. On CR Paneitz operators and CR pluriharmonic functions
  28. Absence of wandering domains for some real entire functions with bounded singular sets
  29. Isomonodromic deformations of logarithmic connections and stability
  30. Pointwise equidistribution with an error rate and with respect to unbounded functions
  31. On the Frobenius stable part of Witt vector cohomology
  32. Quantitative mixing results and inner functions
  33. Spin curves and Scorza quartics
  34. Points rationnels des variétés de Shimura: un principe du “tout ou rien”
  35. On bounded and unbounded global solutions of a supercritical semilinear heat equation
  36. On the Perelman’s reduced entropy and Ricci flat manifolds with maximal volume growth
  37. On Oliver’s p -group conjecture: II
  38. Scattering in the energy space for the NLS with variable coefficients
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