Consider the problem $,-,ext{div}(|abla u|^{p-2}abla u)=|u|^{p^*-2}u ,+,lambda |u|^{q-2}u$ in $B,$ $ u=0 ext{ on $partial B;$}$ where $Bsubset Bbb R^n$ is a ball, $lambda >0$, $10$, we show that there exists $k=k(lambda )in Bbb N$ such that any radial solutions to this problem have at most $k$ nodal curves when $ple q le p^*-1$.
展开▼
机译：考虑问题$ ，-， text {div}（| nabla u | ^ {p-2} nabla u）= | u | ^ {p ^ *-2} u ，+ ， lambda | u | ^ {q-2} u $ in $ B，$ $ u = 0 text {on $ partial B; $} $其中$ B subset Bbb R ^ n $是一个球，$ lambda > 0 $，$ 1 0 $，我们表明在 Bbb N $中存在$ k = k（ lambda），这样当$ p le q时，对该问题的任何径向解最多具有$ k $节点曲线 le p ^ *-1 $。
展开▼
