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 政大典藏 > College of Science > Department of Mathematical Sciences > Periodical Articles >  Item 140.119/120129

 Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/120129

 Title: On nonexistence results for some integro-differential equations of elliptic type Authors: 蔡隆義Tsai, Long-Yi吳水利Wu, Shui Li Contributors: 應數系 Date: 1993-12 Issue Date: 2018-09-25 16:22:57 (UTC+8) Abstract: 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; $$\nabla \cdot[g(|\nabla u|)\nabla u]=K(|x|)h(u)+H(|x|)\int_{\bold R^n}a(|y|)q(u(y))\,dy,\tag2$$ 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),349-385AMS MathSciNet:MR1247556 Data Type: article Appears in Collections: [Department of Mathematical Sciences] Periodical Articles

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