Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/89755
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
上傳時間: 2-May-2016
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\r\nSection 1: Introduction 1-2\r\nSection 2: Some Nonexistence Results for the Positive Solutions 1-4\r\nSection 3: Some Nonexistence Results for the Bounded Solutions 1-40\r\n2. Part II: On Nonexistence Results for Some Quasilinear Equations of Elliptic Type\r\nSection 1: Introduction 2-1\r\nSection 2: Some Nonexistence REsults for Quasilinear Eilliptic Equations 2-2\r\nSection 3: Nonexistence Results for Integro-Differential Equation 2-17\r\n3. Part III: On Nonexistence Results of the Quasilinear Elliptic Equations 3-1\r\nSection 1: Introduction 3-2\r\nSection 2: A More Generalized Pohozeav Inequality 3-3\r\nSection 3: Applications 3-5\r\nSection 4: The Nonexistence of Radial Solution 3-9\r\n4. 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\r\n,Trans. Amer. Math. Soc. 304(1987) , 639-668 .\r\n[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 .\r\n[De]. Devi to C. L. , \"Functional Analysis\" , Academic press, INC. , New York, 1978 .\r\n[H]. Hartman P. , \"Ordinary Differential Equations\" , John Wiley &; Sons. Inc. , New York, 1964 .\r\n[K]. Kusano T . and Swanson C. A. , Radial entire solution of class quasilinear elliptic equations ,Acad.\r\nProc. Inc. January(1989) 379-399.\r\n[Ke] . Keller J. B. , On solutions of△u= f( u) , Comm. Pure Appl. Math. , 10(1957) , 503-510 .\r\n[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 .\r\n[KKN].Kawano N., Kusa no T. and Naito M., On the elliptic equations\r\n△u=(x) u in R2 ,Proc. Amer. Math. Soc. 93( 1985) , 73 - 78 .\r\n[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.\r\n[KO]. Kusano T. and Oharu S. , Bounded entire solutions of second order semilinear elliptic equations\r\nwith application to a parabolic initial value problem , Indiana Univ. Math. J . 34(1985) , 85-95.\r\n[KS]. Kusano T., Naito M. and Swanson C. A. , Radial entire solution of even order semi linear\r\nelliptic equations , Canada. J. Math. 40( 1988) , 1281 - 1300 .\r\n[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 .\r\n[L] . Lin F. -H. , On the elliptic equation Di[aij(X) DjU]-K(x)UP = 0, Proc. Amer. Soc.\r\n95(1985) , 219-226 .\r\n[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.\r\n[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 .\r\n[Mc]. McOwen R. , Conformal metric in [R2 with prescribed Gaussian curvature and positive total curvature , Indiana Univ. Math. J. , 34(1985) , 97-104 .\r\n[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 .\r\n[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 .\r\n[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.\r\n[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.\r\n[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.\r\n[Nt]. Naito M. , A note on bounded positive entire solutions of semilinear elliptic equations, Hiroshima Math. J . , 14(1984) , 211-214.\r\n[S] . Sattinger D. H. , conformal metric in R2 with prescribed curvature ,Indiana. Univ. Math. J. , 22 (1972) , 1- 4 .\r\n[T].Tsai L. - Y., On bounded entire solution of Integro - Differential equations ,Chinese J. Math. 16 (1988) , 265 -288 .\r\n[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
Appears in Collections:學位論文

Files in This Item:
File SizeFormat
index.html115 BHTML2View/Open
Show full item record

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.