论文标题
具有非本地术语的强制性准椭圆不平等的奇异解决方案
Singular solutions for coercive quasilinear elliptic inequalities with nonlocal terms
论文作者
论文摘要
我们研究不等式$$ {\ rm div} \ big（| x |^{ - α} | \ nabla u |^{m-2} \ nabla u \ big） r}^n，$ $ $α> 0 $，$ n \ geq 1 $，$ m> 1 $，$ p，q> m-1 $和$i_β$ and $i_β$表示订单$β\ in（0，n）$的潜在。我们从存在正奇异溶液的这些参数方面获得了鲜明的条件。我们进一步建立了单数解决方案的渐近概况，以$$ a（i_β\ ast u^p） \ quad \ mbox {in} b_1 \ setMinus \ {0 \} \ subset {\ mathbb r}^n，$$，其中$ a \ geq b> 0 $是常数。
We study the inequality $$ {\rm div}\big(|x|^{-α}|\nabla u|^{m-2}\nabla u\big)\geq (I_β\ast u^p)u^q \quad\mbox{ in } B_1\setminus\{0\}\subset {\mathbb R}^N, $$ where $α>0$, $N\geq 1$, $m>1$, $p, q>m-1$ and $I_β$ denotes the Riesz potential of order $β\in(0, N)$. We obtain sharp conditions in terms of these parameters for which positive singular solutions exist. We further establish the asymptotic profile of singular solutions to the double inequality $$ a(I_β\ast u^p)u^q\geq {\rm div}\big(|x|^{-α}|\nabla u|^{m-2}\nabla u\big)\geq b(I_β\ast u^p)u^q \quad\mbox{ in } B_1\setminus\{0\}\subset {\mathbb R}^N, $$ where $a\geq b>0$ are constants.
