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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 26
  3. Calculus of Variations and Partial Differential Equations : Volume 26, Issue 2, June 2006
  4. Nonlinear elliptic equations with large supercritical exponents
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 26, Issue 4, August 2006
Calculus of Variations and Partial Differential Equations : Volume 26, Issue 3, July 2006
Calculus of Variations and Partial Differential Equations : Volume 26, Issue 2, June 2006
Blow-up solutions of inhomogeneous nonlinear Schrödinger equations
Existence of infinitely many solutions for the one-dimensional Perona-Malik model
Nonlinear elliptic equations with large supercritical exponents
Examples for cross curvature flow on 3-manifolds
Entire spacelike hypersurfaces of prescribed scalar curvature in Minkowski space
Calculus of Variations and Partial Differential Equations : Volume 26, Issue 1, May 2006
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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Nonlinear elliptic equations with large supercritical exponents

Content Provider SpringerLink
Author Molle, Riccardo Passaseo, Donato
Copyright Year 2006
Abstract The paper deals with the existence of positive solutions of the problem -Δ u=up in Ω, u=0 on ∂Ω, where Ω is a bounded domain of $$\mathcal{R}^n$$ , n≥ 3, and p>2. We describe new concentration phenomena, which arise as p→ +∞ and can be exploited in order to construct, for p large enough, positive solutions that concentrate, as p→ +∞, near submanifolds of codimension 2. In this paper we consider, in particular, domains with axial symmetry and obtain positive solutions concentrating near (n-2)-dimensional spheres, which approach the boundary of Ω as p→ +∞. The existence and multiplicity results we state allow us to find positive solutions, for large p, also in domains which can be contractible and even arbitrarily close to starshaped domains (while no solution can exist if Ω is starshaped and $$p\ge {2n\over n-2}$$ , as a consequence of the Pohožaev's identity).
Starting Page 201
Ending Page 225
Page Count 25
File Format PDF
ISSN 09442669
Journal Calculus of Variations and Partial Differential Equations
Volume Number 26
Issue Number 2
e-ISSN 14320835
Language English
Publisher Springer-Verlag
Publisher Date 2006-03-08
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Supercritical exponents Concentration phenomena Domain geometry Analysis Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Theoretical, Mathematical and Computational Physics
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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