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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: 2018-09-25 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; $$\nabla \cdot[g(|\nabla u|)\nabla u]=K(|x|)h(u)+H(|x|)\int_{\bold R^n}a(|y|)q(u(y))\,dy,\tag2$$

    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.
    關聯: Chinese Journal of Mathematics,21(4),349-385
    AMS MathSciNet:MR1247556
    資料類型: article
    顯示於類別:[應用數學系] 期刊論文

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