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Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/87366


Title: 單調法在非線性微分方程式之研究
Monotone Methods for Nonlinear Differential Equations
Authors: 張凱君
Chang, Kai-Jiun
Contributors: 蔡隆義
Tsai, Long-Yi
張凱君
Chang, Kai-Jiun
Keywords: 單調法
Monotone method
Date: 1996
Issue Date: 2016-04-28 13:29:57 (UTC+8)
Abstract: 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.
Reference: [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.
Description: 碩士
國立政治大學
應用數學系
83751011
Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002002891
Data Type: thesis
Appears in Collections:[Department of Mathematical Sciences] Theses

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