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| Title | On nonexistence results for some integro-differential equations of elliptic type |
| Creator | 蔡隆義 Tsai, Long-Yi 吳水利 Wu, Shui Li |
| Contributor | 應數系 |
| Date | 1993-12 |
| Date Issued | 25-Sep-2018 16:22:57 (UTC+8) |
| Summary | 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. |
| Relation | Chinese Journal of Mathematics,21(4),349-385 AMS MathSciNet:MR1247556 |
| Type | 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 |