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題名 On nonexistence results for some integro-differential equations of elliptic type
作者 蔡隆義
Tsai, Long-Yi
吳水利
Wu, Shui Li
貢獻者 應數系
日期 1993-12
上傳時間 25-九月-2018 16:22:57 (UTC+8)
摘要 The authors consider the following equations: $$\\Delta u=k(x)h(u)+H(x)\\int_{\\bold R^n}a(y)q(u(y))\\,dy\\tag1$$

in $\\bold R^n$ $(n\\geq 2, \\Delta$ a Laplacian operator), with $h,q$ convex, $K$, $H$ locally Hölder continuous and nonnegative; $$\
abla \\cdot[g(|\
abla u|)\
abla u]=K(|x|)h(u)+H(|x|)\\int_{\\bold R^n}a(|y|)q(u(y))\\,dy,\\tag2$$

where $g$ takes values in some bounded interval $[0,x]$ and its main property is $(pg(p))`>0$.
Their goal is to prove that in both cases no positive and bounded solution exists under additional assumptions. For instance, adding some requirement on the functions $q,h$, it is shown that there is no positive solution of $(1)$ such that its average over $|x|=r$ has a prescribed limit for $r\\to 0$.
The authors prove several theorems of this type. These results are obtained through a series of lower estimates on the average of $u$ which eventually are shown to be inconsistent with the existence of any positive solution.
關聯 Chinese Journal of Mathematics,21(4),349-385
AMS MathSciNet:MR1247556
資料類型 article
dc.contributor 應數系
dc.creator (作者) 蔡隆義
dc.creator (作者) Tsai, Long-Yi
dc.creator (作者) 吳水利
dc.creator (作者) Wu, Shui Li
dc.date (日期) 1993-12
dc.date.accessioned 25-九月-2018 16:22:57 (UTC+8)-
dc.date.available 25-九月-2018 16:22:57 (UTC+8)-
dc.date.issued (上傳時間) 25-九月-2018 16:22:57 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/120129-
dc.description.abstract (摘要) The authors consider the following equations: $$\\Delta u=k(x)h(u)+H(x)\\int_{\\bold R^n}a(y)q(u(y))\\,dy\\tag1$$

in $\\bold R^n$ $(n\\geq 2, \\Delta$ a Laplacian operator), with $h,q$ convex, $K$, $H$ locally Hölder continuous and nonnegative; $$\
abla \\cdot[g(|\
abla u|)\
abla u]=K(|x|)h(u)+H(|x|)\\int_{\\bold R^n}a(|y|)q(u(y))\\,dy,\\tag2$$

where $g$ takes values in some bounded interval $[0,x]$ and its main property is $(pg(p))`>0$.
Their goal is to prove that in both cases no positive and bounded solution exists under additional assumptions. For instance, adding some requirement on the functions $q,h$, it is shown that there is no positive solution of $(1)$ such that its average over $|x|=r$ has a prescribed limit for $r\\to 0$.
The authors prove several theorems of this type. These results are obtained through a series of lower estimates on the average of $u$ which eventually are shown to be inconsistent with the existence of any positive solution.
en_US
dc.format.extent 161 bytes-
dc.format.mimetype text/html-
dc.relation (關聯) Chinese Journal of Mathematics,21(4),349-385
dc.relation (關聯) AMS MathSciNet:MR1247556
dc.title (題名) On nonexistence results for some integro-differential equations of elliptic type
dc.type (資料類型) article