论文标题
关于$φ$ -laplacian的差异不平等解决方案的爆破条件
On blow-up conditions for solutions of differential inequalities with $φ$-Laplacian
论文作者
论文摘要
让$ω\ ne \ emptySet $为$ {\ mathbb r}^n $，$ n \ ge 2 $的无界开放子集。我们获得了问题$$的非负解决方案的爆炸条件 {\ Mathcal L}_φU \ ge F（x，u） \ Quad \ mbox {in} ω， \ Quad \左边。 你 \ right | _ { \部分ω } = 0，$$，其中$φ$和$ f $是某些功能和$$ {\ Mathcal L}_φU = \ operatorname {div} \左边（ \ frac { φ（| \ nabla u |） } { | \ nabla u | } \ nabla u \ right）$$是$φ$ -laplace运算符。
Let $Ω\ne \emptyset$ be an unbounded open subset of ${\mathbb R}^n$, $n \ge 2$. We obtain blow-up conditions for non-negative solutions of the problem $$ {\mathcal L}_φu \ge F (x, u) \quad \mbox{in } Ω, \quad \left. u \right|_{ \partial Ω } = 0, $$ where $φ$ and $F$ are some function and $$ {\mathcal L}_φu = \operatorname{div} \left( \frac{ φ(|\nabla u|) }{ |\nabla u| } \nabla u \right) $$ is the $φ$-Laplace operator.
