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 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: 2016-04-28 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 顯示於類別: [應用數學系] 學位論文

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