TY - JOUR
AU - Furtado, Marcelo F.
PY - 2007/03/01
Y2 - 2023/03/27
TI - Nodal solutions for a nonhomogeneous elliptic equation with symmetry
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 29
IS - 1
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2007.004
SP - 69 - 78
AB - We consider the semilinear problem $-\Delta u + \lambda u =|u|^{p-2}u +f(u)$ in $\Omega$, $u=0$ on $\partial \Omega$ where $\Omega \subset{\mathbb R}^N$ is a bounded smooth domain, $2< p< 2^*=2N/(N-2)$ and $f(t)$behaves like $t^{p-1-\varepsilon}$ at infinity. We show that if $\Omega$ isinvariant by a nontrivial orthogonal involution then, for $\lambda> 0$sufficiently large, the equivariant topology of $\Omega$ is related with thenumber of solutions which change sign exactly once. The results are proved byusing equivariant Lusternik-Schnirelmann theory.
ER -