1. NCCU Academic Hub
  2. Publications
  3. College of Science
  4. Theses
  5. Item

Publications-Theses

Article View/Open

Publication Export

Google ScholarTM

NCCU Library

Citation Infomation

Related Publications in TAIR

題名 單調法在非線性微分方程式之研究
Monotone Methods for Nonlinear Differential Equations
作者 張凱君
Chang, Kai-Jiun
貢獻者 蔡隆義
Tsai, Long-Yi
張凱君
Chang, Kai-Jiun
關鍵詞 單調法
Monotone method
日期 1996
上傳時間 28-Apr-2016 13:29:57 (UTC+8)
摘要 本文旨在討論非線性拋物型積分微分方程式(組)的解之存在性．首先藉由與上解及下解相關的若干假設，我們得到一個比較性的結果．然後我們利用單調法建構出兩個單調收歛到方程式解的序列，從而驗證了方程式解的存在性．
In this paper, the existence of the solutions for nonlinear integro-differential equations and systems is discussed. First, by the assumption of weak upper and weak lower solutions for the given problem, we obtain the comparison result. Next, we provide the method of monotony and construct two sequences which converge monotonically to the solution.
參考文獻 [1] R. A. Adams, Sobolev Spaces, Academic Press, London, 1975.
     [2] S. Carl, L6sung semilinear parabolischer Rand-Anfangswert problem durch monotone Iteration im Sobolevraum (Qr), Z. Anal. Anwendungen, Vol. 5, 237-251,1986.
     [3] S. Carl, A monotone iterative scheme for nonlinear reaction-diffusion systems having nonmonotone reaction terms, 1. Math. Anal. Appl. Vol. 134, 81-93, 1988.
     [4] H. Gajewski, K Gr6ger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974.
     [5] J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, 1971.
     [6] C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992.
     [7] V. P. Politjukov, On the theory of upper and lower solutions and the solvability of quasi linear integro-differential equations, Math.USSR. Sbornik. Vol. 35,499-507, 1979.
     [8] L. Y. Tsai, On integro-differential equations of parabolic type, Bull. Inst. Math. Acad . Sinica, 311-320, 1981.
     [9] L. Y Tsai, Existence of solutions for parabolic integro-ditlerential systems, Sino Japanese.joint seminar on POE, Academic, Sinica, 1990.
     [10] L. Y Tsai, Comparison and stability results for parabolic integro-differential equations, Proc. international Math. conference ,94, World Scientific, 203-218, 1996
     [11] E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. II I A Springer-Verlag, Berlin, 1990.
描述 碩士
國立政治大學
應用數學系
83751011
資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002002891
資料類型 thesis
dc.contributor.advisor 蔡隆義zh_TW
dc.contributor.advisor Tsai, Long-Yien_US
dc.contributor.author (Authors) 張凱君zh_TW
dc.contributor.author (Authors) Chang, Kai-Jiunen_US
dc.creator (作者) 張凱君zh_TW
dc.creator (作者) Chang, Kai-Jiunen_US
dc.date (日期) 1996en_US
dc.date.accessioned 28-Apr-2016 13:29:57 (UTC+8)-
dc.date.available 28-Apr-2016 13:29:57 (UTC+8)-
dc.date.issued (上傳時間) 28-Apr-2016 13:29:57 (UTC+8)-
dc.identifier (Other Identifiers) B2002002891en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/87366-
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 (描述) 83751011zh_TW
dc.description.abstract (摘要) 本文旨在討論非線性拋物型積分微分方程式(組)的解之存在性．首先藉由與上解及下解相關的若干假設，我們得到一個比較性的結果．然後我們利用單調法建構出兩個單調收歛到方程式解的序列，從而驗證了方程式解的存在性．zh_TW
dc.description.abstract (摘要) In this paper, the existence of the solutions for nonlinear integro-differential equations and systems is discussed. First, by the assumption of weak upper and weak lower solutions for the given problem, we obtain the comparison result. Next, we provide the method of monotony and construct two sequences which converge monotonically to the solution.en_US
dc.description.tableofcontents 0 Introduction.1
     1 Monotone methods for nonlinear integral-differential equations．．．．．．．2
     1.1 Preliminaries and hypotheses．．．．．．．．．．2
     1.2 A comparison result．．．．．．．．．．5
     1.3 Existence result via monotone method．．．．．．．．．．8
     2 Monotone methods for nonlinear integro-differential systems．．．．．．．13
     2.1 Preliminaries and hypotheses．．．．．．．．．．13
     2.2 A comparison result．．．．．．．．．．16
     2.3 Existence result via monotone method．．．．．．．．．．19
     References．．．．．．．．．．23		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002002891en_US
dc.subject (關鍵詞) 單調法zh_TW
dc.subject (關鍵詞) Monotone methoden_US
dc.title (題名) 單調法在非線性微分方程式之研究zh_TW
dc.title (題名) Monotone Methods for Nonlinear Differential Equationsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] R. A. Adams, Sobolev Spaces, Academic Press, London, 1975.
     [2] S. Carl, L6sung semilinear parabolischer Rand-Anfangswert problem durch monotone Iteration im Sobolevraum (Qr), Z. Anal. Anwendungen, Vol. 5, 237-251,1986.
     [3] S. Carl, A monotone iterative scheme for nonlinear reaction-diffusion systems having nonmonotone reaction terms, 1. Math. Anal. Appl. Vol. 134, 81-93, 1988.
     [4] H. Gajewski, K Gr6ger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974.
     [5] J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, 1971.
     [6] C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992.
     [7] V. P. Politjukov, On the theory of upper and lower solutions and the solvability of quasi linear integro-differential equations, Math.USSR. Sbornik. Vol. 35,499-507, 1979.
     [8] L. Y. Tsai, On integro-differential equations of parabolic type, Bull. Inst. Math. Acad . Sinica, 311-320, 1981.
     [9] L. Y Tsai, Existence of solutions for parabolic integro-ditlerential systems, Sino Japanese.joint seminar on POE, Academic, Sinica, 1990.
     [10] L. Y Tsai, Comparison and stability results for parabolic integro-differential equations, Proc. international Math. conference ,94, World Scientific, 203-218, 1996
     [11] E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. II I A Springer-Verlag, Berlin, 1990.		zh_TW