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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 13
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 13, Issue 4, December 2006
  4. On a biharmonic equation involving nearly critical exponent
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 13, Issue 5-6, July 2007
Nonlinear Differential Equations and Applications NoDEA : Volume 13, Issue 4, December 2006
Global stability of the Armstrong-Frederick model with periodic biaxial inputs
On a mathematical model of a coupled fluid-structure problem
A remark on Serrin’s Theorem
Decay rate of the range component of solutions to some semilinear evolution equations
A limit problem in natural convection
On equivariant self-similar wave maps
On a biharmonic equation involving nearly critical exponent
Nonlinear Differential Equations and Applications NoDEA : Volume 13, Issue 3, November 2006
Nonlinear Differential Equations and Applications NoDEA : Volume 13, Issue 2, July 2006
Nonlinear Differential Equations and Applications NoDEA : Volume 13, Issue 1, March 2006
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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On a biharmonic equation involving nearly critical exponent

Content Provider SpringerLink
Author Ayed, Mohamed Ben Mehdi, Khalil El
Copyright Year 2006
Abstract This paper is concerned with a biharmonic equation under the Navier boundary condition $${(P_{\mp\varepsilon}): \Delta^{2}u = u^{\frac{n+4}{n-4}\mp\varepsilon}}$$ , u > 0 in Ω and u = Δu = 0 on ∂Ω, where Ω is a smooth bounded domain in $${\mathbb{R}^n}$$ , n ≥ 5, and ε > 0. We study the asymptotic behavior of solutions of (P −ε) which are minimizing for the Sobolev quotient as ε goes to zero. We show that such solutions concentrate around a point x 0 ∈Ω as ε → 0, moreover x 0 is a critical point of the Robin’s function. Conversely, we show that for any nondegenerate critical point x 0 of the Robin’s function, there exist solutions of (P −ε) concentrating around x 0 as ε → 0. Finally we prove that, in contrast with what happened in the subcritical equation (P −ε), the supercritical problem (P +ε) has no solutions which concentrate around a point of Ω as ε → 0.
Ending Page 509
Page Count 25
Starting Page 485
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 4
Volume Number 13
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2006-01-01
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword noncompact variational problems Boundary value problems for higher-order elliptic equations Analysis Nonlinear boundary value problems for linear elliptic equations Elliptic PDEs critical Sobolev exponent Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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