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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

10.1007/978-94-011-0479-1_1

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1432-1807

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On bounded and unbounded global solutions of a sup

Authors: Peter Polá č ik Eiji Yanagida
Publish Date: 2003/10/30
Volume: 327, Issue: 4, Pages: 745-771
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Abstract

We consider the Cauchy problem where u 0 ∈C 0 ℝ N the space of all continuous functions on ℝ N that decay to zero at infinity and p is supercritical in the sense that N≥11 and pge N224N+8sqrtN1/N2N10 We first examine the domain of attraction of steady states and also of general solutions in a class of admissible functions In particular we give a sharp condition on the initial function u 0 so that the solution of the above problem converges to a given steady state Then we consider the asymptotic behavior of global solutions bounded above and below by classical steady states such solutions have compact trajectories in C 0 ℝ N under the supremum norm Our main result reveals an interesting possibility the solution may approach a continuum of steady states not settling down to any particular one of them Finally we prove the existence of global unbounded solutions a phenomenon that does not occur for Sobolevsubcritical exponents

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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. Configuration spaces, transfer, and 2-nodal solutions of a semiclassical nonlinear Schrödinger equation
  34. Spin curves and Scorza quartics
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