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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 19
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 3, June 2012
  4. Ground state and multiple solutions for a critical exponent problem
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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 19, Issue 6, December 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 5, October 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 4, August 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 3, June 2012
Ground state and multiple solutions for a critical exponent problem
Nontrivial solutions to boundary value problems for semilinear strongly degenerate elliptic differential equations
Addendum to: Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem, NoDEA. Nonlinear Differential Equations Appl. 11 (2004), no. 3, 379-391, and a comment on the generalized Ambrosetti-Rabinowitz condition
Periodic problems with double resonance
The fast diffusion equation with measure data
On a class of non-uniformly elliptic equations
Local existence and uniqueness in the largest critical space for a surface growth model
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 2, April 2012
Nonlinear Differential Equations and Applications NoDEA : Volume 19, Issue 1, February 2012
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 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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Ground state and multiple solutions for a critical exponent problem

Content Provider SpringerLink
Author Chen, Z. Shioji, N. Zou, W.
Copyright Year 2011
Abstract We study the following Brezis–Nirenberg type critical exponent equation which is related to the Yamabe problem: $$-\Delta u=\lambda u+ |u|^{2^{\ast}-2}u, \quad u\in H_0^1 (\Omega),$$ where Ω is a smooth bounded domain in $${{\mathbb R}^N(N\ge3)}$$ and 2* is the critical Sobolev exponent. We show that, if N ≥ 5, this problem has at least $${\lceil\frac{N+1}{2}\rceil}$$ pairs of nontrivial solutions for each fixed λ ≥ λ1, where λ1 is the first eigenvalue of −Δ with the Dirichlet boundary condition. For N ≥ 3, we give energy estimates from below for ground state solutions.
Ending Page 277
Page Count 25
Starting Page 253
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 3
Volume Number 19
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2011-07-09
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Boundary value problems for second-order elliptic equations Analysis Variational methods for second-order elliptic equations Nonlinear elliptic equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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