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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; $$\ abla \\cdot[g(\|\ abla u\|)\ abla u]=K(\|x\|)h(u)+H(\|x\|)\\int_{\\bold R^n}a(\|y\|)q(u(y))\\,dy,\\tag2$$ 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
Data Type:	article
Appears in Collections:	[應用數學系] 期刊論文

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