TY - JOUR
T1 - Nonradial Solutions of a Mixed Concave-convex Elliptic Problem
JO - Journal of Partial Differential Equations
VL - 4
SP - 313
EP - 323
PY - 2011
DA - 2011/11
SN - 24
DO - http://doi.org/10.4208/jpde.v24.n4.3
UR - https://global-sci.org/intro/article_detail/jpde/5213.html
KW - Group invariance
KW - nonlinear elliptic equations
KW - variational method
KW - Brezis-Nirenberg problem
KW - eigenvalue and eigenfunction problems
AB - <p>We study the homogeneous Dirichlet problem in a ball for semi-linear elliptic problems derived from the Brezis-Nirenberg one with concave-convex nonlinearities. We are interested in determining non-radial solutions which are invariant with respect to some subgroup of the orthogonal group. We prove that unlike separated nonlinearities, there are two types of solutions, one converging to zero and one diverging. We conclude at the end on the classification of non radial solutions related to the nonlinearity used.</p>