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題名 二階橢圓型偏微分方程式解的不存在性之研究
On nonexistence of second order elliptic partial differentail equations作者 吳水利
WU, SHUI-LI貢獻者 蔡隆義
CAI, LONG-YI
吳水利
WU, SHUI-LI關鍵詞 不存在性
正放射性解
微分方程式
NONEXISTENCE
PARTIAL DIFFERENTAIL EQUATION日期 1992
1991上傳時間 2-May-2016 17:07:11 (UTC+8) 摘要 本文主要在考慮某類二階橢圓型偏微分方程式解的不存在問題，共分為三部分。
1. Part I: On Nonexistence Results for Some Integro-differential Equations of Elliptic Type 1-1 Section 1: Introduction 1-2 Section 2: Some Nonexistence Results for the Positive Solutions 1-4 Section 3: Some Nonexistence Results for the Bounded Solutions 1-40 2. Part II: On Nonexistence Results for Some Quasilinear Equations of Elliptic Type Section 1: Introduction 2-1 Section 2: Some Nonexistence REsults for Quasilinear Eilliptic Equations 2-2 Section 3: Nonexistence Results for Integro-Differential Equation 2-17 3. Part III: On Nonexistence Results of the Quasilinear Elliptic Equations 3-1 Section 1: Introduction 3-2 Section 2: A More Generalized Pohozeav Inequality 3-3 Section 3: Applications 3-5 Section 4: The Nonexistence of Radial Solution 3-9 4. References 4-1參考文獻 [C]. Cheng K. S. and Lin J. T. , On the elliptic equations △u=K(x)u and △u= K(x) e2 u ,Trans. Amer. Math. Soc. 304(1987) , 639-668 . [D]. Ding W. Y. and Ni W. M., On the elliptic equation △u=K(x)u n-2分之n+2 = 0 and related topics, DUKE math. J. 52(1985) , 485-506 . [De]. Devi to C. L. , "Functional Analysis" , Academic press, INC. , New York, 1978 . [H]. Hartman P. , "Ordinary Differential Equations" , John Wiley &; Sons. Inc. , New York, 1964 . [K]. Kusano T . and Swanson C. A. , Radial entire solution of class quasilinear elliptic equations ,Acad. Proc. Inc. January(1989) 379-399. [Ke] . Keller J. B. , On solutions of△u= f( u) , Comm. Pure Appl. Math. , 10(1957) , 503-510 . [KK] . Kawano N. and Kusano T. On the positive entire solutions of a class of second order semilinear elliptic systems , Math. Z. 186(1984), 287-297 . [KKN].Kawano N., Kusa no T. and Naito M., On the elliptic equations △u=(x) u in R2 ,Proc. Amer. Math. Soc. 93( 1985) , 73 - 78 . [KN] . Kusano T., Naito M. and Swanson C. A. , Radial entire solution to even order semilinear elliptic equations in the plane, Proc. Roy. Soc. Edingburgh Sect. A 105(1987),275-287. [KO]. Kusano T. and Oharu S. , Bounded entire solutions of second order semilinear elliptic equations with application to a parabolic initial value problem , Indiana Univ. Math. J . 34(1985) , 85-95. [KS]. Kusano T., Naito M. and Swanson C. A. , Radial entire solution of even order semi linear elliptic equations , Canada. J. Math. 40( 1988) , 1281 - 1300 . [KSU]. Kusano T. , Swanson C. A. and Usami H. , Pairs of positive solutions of quasilinear elliptic equations in exterior domain , Pacific J. Math. 120(1 985) , 385-399 . [L] . Lin F. -H. , On the elliptic equation Di[aij(X) DjU]-K(x)UP = 0, Proc. Amer. Soc. 95(1985) , 219-226 . [LN]. Li Yi and Ni Wei - Ming, On the existence and symmetry properties of finite total mass solutions of the Matukuma equations , the eddington equation and their generalizations , Arch. Rational Mech. Anal. 108(1989),175 - 194. [M]. McOwen R. , On the equation △u + K(x) e2u= f and prescribed negative curvature in R2, J. Math. Anal. Appl. , 103(1984) , 365-370 . [Mc]. McOwen R. , Conformal metric in [R2 with prescribed Gaussian curvature and positive total curvature , Indiana Univ. Math. J. , 34(1985) , 97-104 . [N]. Ni W. -M. , On the elliptic equation △u=K(x)u n-2分之n+2 = 0 ,its generalizations and applications in geometry, Indian. Univ. Math. J . 31 (1982) ,493-529 . [Ni]. Ni W. -M. , On the elliptic equation △u + K(x) e2u = 0 and conformal metrics with prescribed Gassian curvatures , Invent. Math. , 66(1982) , 343 - 352 . [NJ] . Ni W. -M. and Serrin J. , Existence and nonexistence throrems for ground states of quasi linear partial differential equations ,the anomalous case, Accad. Naz. dei Lincei. ,77(1986),231 - 257. [NM]. Ni W. -M. and Serrin J., Nonexistence theorems for quasilinear partial differential equations Rendiconti. del Cricoli Mat. di palermo , Series Ⅱ , 8(1985) ,171 - 185. [NS]. Ni W. -M. and Serrin J . ,Nonexistence theorems for singular solution of quasilinear partial differential equations , Pure and Applied Math. Vol. XXXIX, (1986) 397 - 399. [Nt]. Naito M. , A note on bounded positive entire solutions of semilinear elliptic equations, Hiroshima Math. J . , 14(1984) , 211-214. [S] . Sattinger D. H. , conformal metric in R2 with prescribed curvature ,Indiana. Univ. Math. J. , 22 (1972) , 1- 4 . [T].Tsai L. - Y., On bounded entire solution of Integro - Differential equations ,Chinese J. Math. 16 (1988) , 265 -288 . [W]. Wheeden R. C. and Zygmund A. ," Measure and Integral" , ( Monographs and texbooks in pure and applied math. ; 43) , ISBN 0-8247-6499-4 . 描述 碩士
國立政治大學
應用數學系資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002004731 資料類型 thesis dc.contributor.advisor 蔡隆義 zh_TW dc.contributor.advisor CAI, LONG-YI en_US dc.contributor.author (Authors) 吳水利 zh_TW dc.contributor.author (Authors) WU, SHUI-LI en_US dc.creator (作者) 吳水利 zh_TW dc.creator (作者) WU, SHUI-LI en_US dc.date (日期) 1992 en_US dc.date (日期) 1991 en_US dc.date.accessioned 2-May-2016 17:07:11 (UTC+8) - dc.date.available 2-May-2016 17:07:11 (UTC+8) - dc.date.issued (上傳時間) 2-May-2016 17:07:11 (UTC+8) - dc.identifier (Other Identifiers) B2002004731 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/89755 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系 zh_TW dc.description.abstract (摘要) 本文主要在考慮某類二階橢圓型偏微分方程式解的不存在問題，共分為三部分。 zh_TW dc.description.abstract (摘要) 1. Part I: On Nonexistence Results for Some Integro-differential Equations of Elliptic Type 1-1 Section 1: Introduction 1-2 Section 2: Some Nonexistence Results for the Positive Solutions 1-4 Section 3: Some Nonexistence Results for the Bounded Solutions 1-40 2. Part II: On Nonexistence Results for Some Quasilinear Equations of Elliptic Type Section 1: Introduction 2-1 Section 2: Some Nonexistence REsults for Quasilinear Eilliptic Equations 2-2 Section 3: Nonexistence Results for Integro-Differential Equation 2-17 3. Part III: On Nonexistence Results of the Quasilinear Elliptic Equations 3-1 Section 1: Introduction 3-2 Section 2: A More Generalized Pohozeav Inequality 3-3 Section 3: Applications 3-5 Section 4: The Nonexistence of Radial Solution 3-9 4. References 4-1 - dc.description.tableofcontents 1. Part I: On Nonexistence Results for Some Integro-differential Equations of Elliptic Type 1-1 Section 1: Introduction 1-2 Section 2: Some Nonexistence Results for the Positive Solutions 1-4 Section 3: Some Nonexistence Results for the Bounded Solutions 1-40 2. Part II: On Nonexistence Results for Some Quasilinear Equations of Elliptic Type Section 1: Introduction 2-1 Section 2: Some Nonexistence REsults for Quasilinear Eilliptic Equations 2-2 Section 3: Nonexistence Results for Integro-Differential Equation 2-17 3. Part III: On Nonexistence Results of the Quasilinear Elliptic Equations 3-1 Section 1: Introduction 3-2 Section 2: A More Generalized Pohozeav Inequality 3-3 Section 3: Applications 3-5 Section 4: The Nonexistence of Radial Solution 3-9 4. References 4-1 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002004731 en_US dc.subject (關鍵詞) 不存在性 zh_TW dc.subject (關鍵詞) 正放射性解 zh_TW dc.subject (關鍵詞) 微分方程式 zh_TW dc.subject (關鍵詞) NONEXISTENCE en_US dc.subject (關鍵詞) PARTIAL DIFFERENTAIL EQUATION en_US dc.title (題名) 二階橢圓型偏微分方程式解的不存在性之研究 zh_TW dc.title (題名) On nonexistence of second order elliptic partial differentail equations en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [C]. Cheng K. S. and Lin J. T. , On the elliptic equations △u=K(x)u and △u= K(x) e2 u ,Trans. Amer. Math. Soc. 304(1987) , 639-668 . [D]. Ding W. Y. and Ni W. M., On the elliptic equation △u=K(x)u n-2分之n+2 = 0 and related topics, DUKE math. J. 52(1985) , 485-506 . [De]. Devi to C. L. , "Functional Analysis" , Academic press, INC. , New York, 1978 . [H]. Hartman P. , "Ordinary Differential Equations" , John Wiley &; Sons. Inc. , New York, 1964 . [K]. Kusano T . and Swanson C. A. , Radial entire solution of class quasilinear elliptic equations ,Acad. Proc. Inc. January(1989) 379-399. [Ke] . Keller J. B. , On solutions of△u= f( u) , Comm. Pure Appl. Math. , 10(1957) , 503-510 . [KK] . Kawano N. and Kusano T. On the positive entire solutions of a class of second order semilinear elliptic systems , Math. Z. 186(1984), 287-297 . [KKN].Kawano N., Kusa no T. and Naito M., On the elliptic equations △u=(x) u in R2 ,Proc. Amer. Math. Soc. 93( 1985) , 73 - 78 . [KN] . Kusano T., Naito M. and Swanson C. A. , Radial entire solution to even order semilinear elliptic equations in the plane, Proc. Roy. Soc. Edingburgh Sect. A 105(1987),275-287. [KO]. Kusano T. and Oharu S. , Bounded entire solutions of second order semilinear elliptic equations with application to a parabolic initial value problem , Indiana Univ. Math. J . 34(1985) , 85-95. [KS]. Kusano T., Naito M. and Swanson C. A. , Radial entire solution of even order semi linear elliptic equations , Canada. J. Math. 40( 1988) , 1281 - 1300 . [KSU]. Kusano T. , Swanson C. A. and Usami H. , Pairs of positive solutions of quasilinear elliptic equations in exterior domain , Pacific J. Math. 120(1 985) , 385-399 . [L] . Lin F. -H. , On the elliptic equation Di[aij(X) DjU]-K(x)UP = 0, Proc. Amer. Soc. 95(1985) , 219-226 . [LN]. Li Yi and Ni Wei - Ming, On the existence and symmetry properties of finite total mass solutions of the Matukuma equations , the eddington equation and their generalizations , Arch. Rational Mech. Anal. 108(1989),175 - 194. [M]. McOwen R. , On the equation △u + K(x) e2u= f and prescribed negative curvature in R2, J. Math. Anal. Appl. , 103(1984) , 365-370 . [Mc]. McOwen R. , Conformal metric in [R2 with prescribed Gaussian curvature and positive total curvature , Indiana Univ. Math. J. , 34(1985) , 97-104 . [N]. Ni W. -M. , On the elliptic equation △u=K(x)u n-2分之n+2 = 0 ,its generalizations and applications in geometry, Indian. Univ. Math. J . 31 (1982) ,493-529 . [Ni]. Ni W. -M. , On the elliptic equation △u + K(x) e2u = 0 and conformal metrics with prescribed Gassian curvatures , Invent. Math. , 66(1982) , 343 - 352 . [NJ] . Ni W. -M. and Serrin J. , Existence and nonexistence throrems for ground states of quasi linear partial differential equations ,the anomalous case, Accad. Naz. dei Lincei. ,77(1986),231 - 257. [NM]. Ni W. -M. and Serrin J., Nonexistence theorems for quasilinear partial differential equations Rendiconti. del Cricoli Mat. di palermo , Series Ⅱ , 8(1985) ,171 - 185. [NS]. Ni W. -M. and Serrin J . ,Nonexistence theorems for singular solution of quasilinear partial differential equations , Pure and Applied Math. Vol. XXXIX, (1986) 397 - 399. [Nt]. Naito M. , A note on bounded positive entire solutions of semilinear elliptic equations, Hiroshima Math. J . , 14(1984) , 211-214. [S] . Sattinger D. H. , conformal metric in R2 with prescribed curvature ,Indiana. Univ. Math. J. , 22 (1972) , 1- 4 . [T].Tsai L. - Y., On bounded entire solution of Integro - Differential equations ,Chinese J. Math. 16 (1988) , 265 -288 . [W]. Wheeden R. C. and Zygmund A. ," Measure and Integral" , ( Monographs and texbooks in pure and applied math. ; 43) , ISBN 0-8247-6499-4 . zh_TW
