Solutions of elliptic equations involving critical Sobolev exponents with neumann boundary conditions |
| |
Authors: | Myriam Comte Mariette C Knaap |
| |
Institution: | (1) Laboratoire d'Analyse Numérique, Tour 55-65, 5e etage, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cédex 05, France;(2) Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands |
| |
Abstract: | We consider the problem −Δu=|u|
p−1u+λu in Ω with
on δΩ, where Ω is a bounded domain inR
N
,p=(N+2)/(N−2) is the critical Sobolev exponent,n the outward pointing normal and λ a constant. Our main result is that if Ω is a ball inR
N
, then for every λ∈R the problem admits infinitely many solutions. Next we prove that for every bounded domain Ω inR
3, symmetric with respect to a plane, there exists a constant μ>0 such that for every λ<μ this problem has at least one non-trivial
solution.
This work was supported by the Paris VI-Leiden exchange program
Supported by the Netherlands organisation for scientific research NWO, under number 611-306-016. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|