scholarly journals Existence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zonghu Xiu
Keyword(s):  
Elliptic Problem ◽  
Multiple Solutions ◽  
Critical Sobolev Exponent ◽  
Sobolev Exponent

Multiplicity of non-radial solutions of critical elliptic problems in an annulus

2005 ◽  
Vol 135 (1) ◽  
pp. 25-37 ◽  
Author(s):  
Djairo Guedes de Figueiredo ◽  
Olímpio Hiroshi Miyagaki
Keyword(s):  
Critical Points ◽  
Elliptic Problem ◽  
Elliptic Problems ◽  
Critical Sobolev Exponent ◽  
Radial Solutions ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Sobolev Exponent ◽  
Image Position

By looking for critical points of functionals defined in some subspaces of , invariant under some subgroups of O (N), we prove the existence of many positive non-radial solutions for the following semilinear elliptic problem involving critical Sobolev exponent on an annulus, where 2* − 1 := (N + 2)/(N − 2) (N ≥ 4), the domain is an annulus and f : R+ × R+ → R is a C1 function, which is a subcritical perturbation.

A NONEXISTENCE RESULT OF SINGLE PEAKED SOLUTIONS TO A SUPERCRITICAL NONLINEAR PROBLEM

2003 ◽  
Vol 05 (02) ◽  
pp. 179-195 ◽  
Author(s):  
M. BEN AYED ◽  
K. EL MEHDI ◽  
O. REY ◽  
M. GROSSI
Keyword(s):  
Bounded Domain ◽  
Elliptic Problem ◽  
Critical Sobolev Exponent ◽  
Positive Parameter ◽  
Nonlinear Elliptic Problem ◽  
Smooth Bounded Domain ◽  
Nonlinear Elliptic ◽  
Nonexistence Result ◽  
Small Positive Parameter ◽  
Sobolev Exponent

This paper is concerned with the nonlinear elliptic problem (Pε): -Δu = up+ε, u > 0 in Ω; u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝn, n ≥ 3, p + 1 = 2n/(n - 2) is the critical Sobolev exponent and ε is a small positive parameter. In contrast with the subcritical problem (P- ε) studied by Han [11] and Rey [17], we show that (Pε) has no single peaked solution for small ε.

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