Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (5): 559-564.
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(College of Science and engineering, Hainan University, Haikou 570228)
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Abstract:
In this paper, by using certain fixed points theorem based on the degree theory, some sufficient conditions for the existence of solutions of initial and boundary value problems for n order ordinary differential equations in Banach spaces are given, moreover, the authors get existence of maximal and minimal solutions. The results are extension of reference [1-2].
Key words: Boundary value problems, Set-contract operators, Fixed points, Non- compactness measures.
CLC Number:
Hong Shihuang Ou Yigui. On the Solvability of Initial and Boundary Value Problems for High Order Ordinary Differential Equations in Banach Spaces[J].Acta mathematica scientia,Series A, 1999, 19(5): 559-564.
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１ ＤｅｉｍｌｉｎｇＫ．ＯｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｉｎＢａｎａｃｈｓｐａｃｅｓ．Ｂｅｒｌｉｎ，Ｎｅｗ Ｙｏｒｋ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９７７ ２ 林壮鹏．抽象空间中微分方程的一类饱和最大，最小解的存在性．数学学报，１９９２，（１）：１３４－１３９ ３ Ｎｋａｓｈａｍａ Ｍ Ｎ，ＳａｎｔａｎｉｌｌａＪ．Ｅｘｉｓｔｅｎｃｅｏｆｍｕｌｌｔｉｐｌｅｓｏｌｕｔｉｏｎｓｏｆｓｏｍｅｎｏｎｌｉｎｅａｒｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓ．ＪＤｉｆｆＥｑｕｓ，１９９０，８４：１４８－１６４ ４ 胡适耕．非线性分析．武汉：华中理工大学出版社，１９９６ ５ ＧｕｏＤａｊｕｎ．ＥｘｔｒｅｍａｌｓｏｌｕｔｉｏｎｓｏｆｎｏｎｌｉｎｅａｒＦｒｅｄｈｏｌｍｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎｓｉｎＢａｎａｃｈｓｐａｃｅｓ．Ｎｏｒｔｈｅａｓｔｅｒｎ ＭａｔｈＪ，１９９１，７（４）：４１６－４２３ ６ 洪世煌，胡适耕．Ｂａｎａｃｈ空间中二阶常微分方程初值问题的解的存在唯一性．应用数学和力学，１９９９，（３）：１３５－１４４ ７ Ｏ＇ＲｅｇａｎＤ．Ｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｓｆｏｒｎｏｎｌｉｎｅａｒｏｐｅｒａｔｏｒｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９６，２０２（２）：４５５－４６４
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