TY - JOUR
T1 - A critical elliptic problem for polyharmonic operators
AU - Ge, Yuxin
AU - Wei, Juncheng
AU - Zhou, Feng
PY - 2011/4/15
Y1 - 2011/4/15
N2 - In this paper, we study the existence of solutions for a critical elliptic problem for polyharmonic operators. We prove the existence result in some general domain by minimizing on some infinite-dimensional Finsler manifold for some suitable perturbation of the critical nonlinearity when the dimension of domain is larger than critical one. For the critical dimensions, we prove also the existence of solutions in domains perforated with the small holes. Some unstable solutions are obtained at higher level sets by Coron's topological method, provided that the minimizing solution does not exist.
AB - In this paper, we study the existence of solutions for a critical elliptic problem for polyharmonic operators. We prove the existence result in some general domain by minimizing on some infinite-dimensional Finsler manifold for some suitable perturbation of the critical nonlinearity when the dimension of domain is larger than critical one. For the critical dimensions, we prove also the existence of solutions in domains perforated with the small holes. Some unstable solutions are obtained at higher level sets by Coron's topological method, provided that the minimizing solution does not exist.
KW - Critical and non-critical dimensions
KW - Ground state solutions
KW - Polyharmonic operators
KW - Topological methods
UR - https://www.scopus.com/pages/publications/79551481152
U2 - 10.1016/j.jfa.2011.01.005
DO - 10.1016/j.jfa.2011.01.005
M3 - 文章
AN - SCOPUS:79551481152
SN - 0022-1236
VL - 260
SP - 2247
EP - 2282
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 8
ER -