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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/87366
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dc.contributor.advisor蔡隆義zh_TW
dc.contributor.advisorTsai, Long-Yien_US
dc.contributor.author張凱君zh_TW
dc.contributor.authorChang, Kai-Jiunen_US
dc.creator張凱君zh_TW
dc.creatorChang, Kai-Jiunen_US
dc.date1996en_US
dc.date.accessioned2016-04-28T05:29:57Z-
dc.date.available2016-04-28T05:29:57Z-
dc.date.issued2016-04-28T05:29:57Z-
dc.identifierB2002002891en_US
dc.identifier.urihttp://nccur.lib.nccu.edu.tw/handle/140.119/87366-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用數學系zh_TW
dc.description83751011zh_TW
dc.description.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．zh_TW
dc.description.abstractIn 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.tableofcontents0 Introduction.1\r\n1 Monotone methods for nonlinear integral-differential equations．．．．．．．2\r\n1.1 Preliminaries and hypotheses．．．．．．．．．．2\r\n1.2 A comparison result．．．．．．．．．．5\r\n1.3 Existence result via monotone method．．．．．．．．．．8\r\n2 Monotone methods for nonlinear integro-differential systems．．．．．．．13\r\n2.1 Preliminaries and hypotheses．．．．．．．．．．13\r\n2.2 A comparison result．．．．．．．．．．16\r\n2.3 Existence result via monotone method．．．．．．．．．．19\r\nReferences．．．．．．．．．．23zh_TW
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#B2002002891en_US
dc.subject單調法zh_TW
dc.subjectMonotone methoden_US
dc.title單調法在非線性微分方程式之研究zh_TW
dc.titleMonotone Methods for Nonlinear Differential Equationsen_US
dc.typethesisen_US
dc.relation.reference[1] R. A. Adams, Sobolev Spaces, Academic Press, London, 1975.\r\n[2] S. Carl, L6sung semilinear parabolischer Rand-Anfangswert problem durch monotone Iteration im Sobolevraum (Qr), Z. Anal. Anwendungen, Vol. 5, 237-251,1986.\r\n[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.\r\n[4] H. Gajewski, K Gr6ger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974.\r\n[5] J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, 1971.\r\n[6] C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992.\r\n[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.\r\n[8] L. Y. Tsai, On integro-differential equations of parabolic type, Bull. Inst. Math. Acad . Sinica, 311-320, 1981.\r\n[9] L. Y Tsai, Existence of solutions for parabolic integro-ditlerential systems, Sino Japanese.joint seminar on POE, Academic, Sinica, 1990.\r\n[10] L. Y Tsai, Comparison and stability results for parabolic integro-differential equations, Proc. international Math. conference ,94, World Scientific, 203-218, 1996\r\n[11] E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. II I A Springer-Verlag, Berlin, 1990.zh_TW
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