Acta mathematica scientia,Series A ›› 2000, Vol. 20 ›› Issue (4): 506-512.
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(1 Department of Mathematics, Tianjin University, Tianjin 300072,
2 Department of Mechanics, Tianjin University, Tianjin 300072)
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Abstract:
The existence of global solutions and coupled minimal and maximal quasisolutions are studied for a class of nonlinear integrodifferential equations on the infinite interval R+ in Banach spaces. Some existence theorems of global solutions and coupled minimal and maximal quasisolutions are obtained which improve and generalize the related results in [1-2].
Key words: Integrodifferential equations, Monotone iterative method, Monch fixed point theorem, Kuratowski noncompactness measure.
CLC Number:
Chen Fangqi1,2 Chen Yushu2 Wu Zhiqiang2. Global Solutions of a Class of Nonlinear Integrodifferential Equations in Banach Spaces[J].Acta mathematica scientia,Series A, 2000, 20(4): 506-512.
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１ ＤｕＳ Ｗ，Ｌａｋｓｈｍｉｋａｎｔｈａｍ Ｖ．ＭｏｎｏｔｏｎｅｉｔｅｒａｔｉｖｅｔｅｃｈｎｉｑｕｅｆｏｒｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｉｎＢａｎａｃｈｓｐａｃｅｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９８２，８７：４５４－４５９ ２ ＧｕｏＤａｊｕｎ．ＩｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｉｎｔｅｇｒｏｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｏｆＶｏｌｔｅｒｒａｔｙｐｅｉｎＢａｎａｃｈｓｐａｃｅｓ．ＪＡｐｐｌＭａｔｈＳｔｏｃｈＡｎａｌ，１９９４，７：１３－２３ ３ Ｇｕｏ Ｄａｊｕｎ，Ｌａｋｓｈｍｉｋａｎｔｈａｍ Ｖ．Ｃｏｕｐｌｅｄｆｉｘｅｄｐｏｉｎｔｓｏｆｎｏｎｌｉｎｅａｒｏｐｅｒａｔｏｒｓ ｗｉｔｈａｐｐｌｉｃａｔｉｏｎｓ．Ｎｏｎｌｉｎｅａｒ Ａｎａｌ，１９８７，１１：６２３－６３２ ４ ＨｅｉｎｚＨ Ｐ．Ｏｎｔｈｅｂｅｈａｖｉｏｕｒｏｆｍｅａｓｕｒｅｏｆｎｏｎｃｏｍｐａｃｔｎｅｓｓｗｉｔｈｒｅｓｐｅｃｔｔｏｄｉｆｆｅｒｅｎｔｉａｔｉｏｎａｎｄｉｎｔｅｇｒａｔｉｏｎｏｆｖｅｃｔｏｒｖａｌｕｅｄｆｕｎｃｔｉｏｎｓ．ＮｏｎｌｉｎｅａｒＡｎａｌ，１９８３，７：１３５１－１３７１ ５ Ｍ¨ｏｎｃｈＨ．ＢｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｎｏｎｌｉｎｅａｒｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｏｆｓｅｃｏｎｄｏｒｄｅｒｉｎＢａｎａｃｈｓｐａｃｅｓ．ＮｏｎｌｉｎｅａｒＡｎａｌ，１９８０，４：９８５－９９９ ６ ＧｕｏＤａｊｕｎ，Ｌａｋｓｈｍｉｋａｎｔｈａｍ Ｖ，Ｌｉｕ Ｘｉｎｚｈｉ．Ｎｏｎｌｉｎｅａｒｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎｓｉｎａｂｓｔｒａｃｔｓｐｅｃｅｓ．Ｄｏｒｄｒｅｃｈｅｔ／Ｂｏｓｔｏｎ：Ｋｌｕｗｅｒａｃａｄｅｍｉｃｐｕｂｌｉｓｈｅｒｓ，１９９６ ７ ＤｕＹ．ＦｉｘｅｄｐｏｉｎｔｓｏｆｉｎｃｒｅａｓｉｎｇｏｐｅｒａｔｏｒｓｉｎｏｒｄｅｒｅｄＢａｎａｃｈｓｐｅｃｅｓａｎｄａｐｐｌｉｃａｔｉｏｎｓ．ＡｐｐｌＡｎａｌ，１９９０，３８：１－２０ ８ Ｌａｋｓｈｍｉｋａｎｔｈａｍ Ｖ，ＬｅｅｌａＳ．ＤｉｆｆｅｒｅｎｔｉａｌａｎｄＩｎｔｅｇｒａｌＩｎｅｑｕａｌｉｔｉｅｓ．Ｎｅｗ Ｙｏｒｋ：ＡｃａｄｅｍｉｃＰｒｅｓｓ，１９６９ ９ ＣｈｅｎＦａｎｇｑｉ．ＥｘｉｓｔｅｎｃｅｏｆｓｏｌｕｔｉｏｎｓｆｏｒｍｉｘｅｄｍｏｎｏｔｏｎｅｉｍｐｕｌｓｉｖｅＶｏｌｔｅｒｒａｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎｓｉｎＢａｎａｃｈｓｐａｃｅｓ．ＡｃｔａＭａｔｈｅｍａｔｉｃａＳｃｉｅｎｔｉａ，１９９８，１８：３７１－３７８ １０ ＤｅｉｍｌｉｎｇＫ．ＮｏｎｌｉｎｅａｒＦｕｎｃｔｉｏｎａｌＡｎａｌｙｓｉｓ．Ｂｅｒｌｉｎ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９８５ １１ 陈芳启．Ｂａｎａｃｈ空间中混合单调脉冲微分积分方程解的存在性．系统科学与数学，１９９９，１９（１）：１１１－１１５
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