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AN00234610-20190101-0063.pdf
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:512.6 KB
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:Oct 27, 2021 |
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| Title |
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経済学のための常微分方程式入門
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| Kana |
ケイザイガク ノ タメ ノ ジョウビブン ホウテイシキ ニュウモン
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Keizaigaku no tame no jōbibun hōteishiki nyūmon
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An introduction of ordinary differential equations for economists
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細矢, 祐誉
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ホソヤ, ユウキ
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Hosoya, Yūki
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| Affiliation |
関東学院大学経済学部
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College of Economics, Kanto-Gakuin University
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慶應義塾経済学会
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ケイオウ ギジュク ケイザイ ガッカイ
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| Romanization |
Keiō gijuku keizai gakkai
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2019
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三田学会雑誌
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Mita journal of economics
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111
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4
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2019
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1
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435(63)
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461(89)
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| Abstract |
本稿では，正規形の常微分方程式について解説し，その解の局所存在定理を，不動点定理を 用いて示す。存在定理には四種類あるが，本稿ではそれらの違いにそれぞれ触れた上で，全部同じや り方で証明できることを示す。さらに，この証明法以外の存在定理との比較や，経済学における微分 方程式の主な応用について触れる。
This paper explains the standard form ordinary differential equations, and shows local existence theorems of a solution by using fixed point theorems. We explain differences between these four existence theorems, and verify that these theorems can be proved by the same method. Moreover, we compare this proof with other proofs, and introduce applications of the ordinary differential equations in economics.
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| Keyword |
| 縮小写像の不動点定理，シャウダーの不動点定理，ピカール＝リンデレーフの存在定理，ペアノの存在定理，カラテオドリの存在定理
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| Contraction mapping fixed point theorem
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| Schauder’s fixed point theorem
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| Picard-Lindelöf’s existence theorem
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| Peano’s existence theorem
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| Carathéodory’s existence theorem
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| History |
| Apr 8, 2019 | | インデックス を変更 |
| Aug 5, 2019 | | タイトル,別タイトル 名前,抄録 内容,キーワード,キーワード,本文URI URI を変更 |
| Jan 6, 2020 | | Modified; 本文,版. |
| Oct 27, 2021 | | JaLCDOI を変更 |
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