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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-Sep-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-Sep-2018 16:22:57 (UTC+8) - dc.date.available 25-Sep-2018 16:22:57 (UTC+8) - dc.date.issued (上傳時間) 25-Sep-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
