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題名 Nonlinear Elliptic Equations in Unbounded Domains 作者 蔡隆義
Tsai, Long-Yi貢獻者 應數系 日期 1990-03 上傳時間 25-Sep-2018 16:21:56 (UTC+8) 摘要 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. 關聯 Chinese Journal of Mathematics , Vol. 18, No. 1 , pp. 21-44
AMS MathSciNet:MR1052498資料類型 article dc.contributor 應數系 dc.creator (作者) 蔡隆義 dc.creator (作者) Tsai, Long-Yi dc.date (日期) 1990-03 dc.date.accessioned 25-Sep-2018 16:21:56 (UTC+8) - dc.date.available 25-Sep-2018 16:21:56 (UTC+8) - dc.date.issued (上傳時間) 25-Sep-2018 16:21:56 (UTC+8) - dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/120127 - dc.description.abstract (摘要) 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. en_US dc.format.extent 161 bytes - dc.format.mimetype text/html - dc.relation (關聯) Chinese Journal of Mathematics , Vol. 18, No. 1 , pp. 21-44 dc.relation (關聯) AMS MathSciNet:MR1052498 dc.title (題名) Nonlinear Elliptic Equations in Unbounded Domains dc.type (資料類型) article
