论文标题
球上的$ p $ laplace方程的解决方案的存在和独特性
Existence and uniqueness of solutions for a class of $p$-Laplace equations on a ball
论文作者
论文摘要
对于概括模型案例\ [δ_pu-a（r）u^{p-1}+b（r）u^q = 0 \; \; \ mbox {in $ b $}，\; \; u = 0 \; \; \ mbox {on $ \ partial b $}，\]，其中$ b $是$ r^n $，$ n \ geq 1 $，$ r = | x | $，$ p，q> 1 $和$Δ_P$表示$ p $ -p $ - laplace操作员的情况，我们为存在和独立的阳性解决方案提供条件。如果$ n = 1 $，我们给出更一般的结果。
For a class of equations generalizing the model case \[ Δ_p u-a(r)u^{p-1}+b(r)u^q=0 \; \; \mbox{in $B$}, \; \; u=0 \; \; \mbox{on $\partial B$}, \] where $B$ is the unit ball in $R^n$, $n \geq 1$, $r=|x|$, $p,q>1$, and $Δ_p$ denotes the $p$-Laplace operator, we give conditions for the existence and uniqueness of positive solution. In case $n=1$, we give a more general result.
