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https://nccur.lib.nccu.edu.tw/handle/140.119/120127
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| Title: | Nonlinear Elliptic Equations in Unbounded Domains |
| Authors: | 蔡隆義
Tsai, Long-Yi |
| Contributors: | 應數系 |
| Date: | 1990-03 |
| Issue Date: | 2018-09-25 16:21:56 (UTC+8) |
| Abstract: | The author considers nonlinear elliptic second-order integro-differ- ential equations of the form $$ -\\sum_{i=1}^N (\\partial/\\partial x_i) A_i (x,u(x),\
abla u(x))+F (x,u(x), (Ku)(x))=f(x) $$
in an exterior domain $G$ under Dirichlet boundary conditions. The boundary $\\partial G$ is smooth and $\\{A_1,\\cdots, A_N\\}$ satisfy the Leray-Lions conditions in the case $p=2$. The operator $K\\: L_2 (G)\\to L_2(G)$ is nonlinear, bounded, continuous and has a Fréchet derivative which is bounded on bounded subsets of $L_2(G)$. The function $f$ is assumed to belong to the dual space $H^{-1} (G)$. The author establishes the existence of weak solutions using a concept of weak $\\varepsilon$-upper and $\\varepsilon$-lower solutions. Examples are given in which the operator $K$ has the form $\\int_G \\varphi(x,y,u(y))\\,dy$. This work represents a continuation of the author`s previous papers [same journal 11 (1983), no. 1, 75–84; MR0692993; ibid. 14 (1986), no. 3, 163–177; MR0867950]. Mention must also be made of a paper by P. Hartman and G. Stampacchia [Acta Math. 115 (1966), 271–310; MR0206537] in which existence and regularity for these types of equations are studied using different methods. |
| Relation: | Chinese Journal of Mathematics , Vol. 18, No. 1 , pp. 21-44
AMS MathSciNet:MR1052498 |
| Data Type: | article |
| Appears in Collections: | [應用數學系] 期刊論文
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