Banach空间中二阶非线性脉冲微分-积分方程的初值问题

Abstract

Abstract:

Through intrducing the equivalent norm, by applying Banach fixed theorem, under simpler conditions, the author has obtained existence and uniqueness and iterative approximation of solution for initial value problems of nonlinear second order impulsive integrodifferential equations in Banach space, and improved and generalized the corresponding results of paper [5] for d0=0 (J.Math.Anal.Appl. 200(1996),1-13).The assumed condition in present paper is easy to be judged and the method is different essentially from the one in paper [5].

Key words: Ｎｏｎｌｉｎｅａｒｉｍｐｕｌｓｉｖｅｅｑｕａｔｉｏｎ, Ｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍ, Ｂａｎａｃｈｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍ

CLC Number:

３４Ｇ２０，４５Ｊ０５

Chai Guoqing. Initial Value Problems for Nonlinear Second Order Impulsive Integrodifferential Equations in Banach Space[J].Acta mathematica scientia,Series A, 2000, 20(3): 351-359.

Trendmd

References

１　ＬａｋｓｈｍｉｋａｎｔｈａｍＶ，ＢａｉｎｏｖＤＤ，ＳｉｍｅｏｎｏｖＰＳ．Ｔｈｅｏｒｙｏｆｉｍｐｕｌｓｉｖｅｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．Ｓｉｎｇａｐｏｒｅ：ＷｏｒｌｄＳｃｉｅｎｔｉｆｉｃ，１９８９
２　ＧｕｏＤａｊｕｎ，ＬｉｕＸｉｎｚｈｉ．ＥｘｔｒｅｍａｌｓｏｌｕｔｉｏｎｓｏｆｎｏｎｌｉｎｅａｒｉｍｐｕｌｓｉｖｅｉｎｔｅｇｒｏｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｉｎＢａｎａｃｈｓｐａｃｅｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９３，１７７：５３８－５５２
３　ＧｕｏＤａｊｕｎ．ＥｘｉｓｔｅｎｃｅｏｆｓｏｌｕｔｉｏｎｏｆｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｎｏｎｌｉｎｅａｒｓｅｃｏｎｄｏｒｄｅｒｉｍｐｕｌｓｉｖｅｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｉｎＢａｎａｃｈｓｐａｃｅｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９４，１８１：４０７－４２１
４　ＧｕｏＤａｊｕｎ，ＬｉｕＸｉｎｚｈｉ．Ｍｕｌｔｉｐｌｅｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｏｆｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｉｍｐｕｌｓｉｖｅｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＮｏｎｌｉｎｅａｒＡｎａｌ，１９９５，２５：３２７－３３７
５　ＧｕｏＤａｊｕｎ．ＩｎｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｎｏｎｌｉｎｅａｒｓｅｃｏｎｄｏｒｄｅｒｉｍｐｕｌｓｉｖｅｉｎｔｅｇｒｏｄｅｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｉｎＢａｎａｃｈｓｐａｃｅｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９６，２００：１－１３
６　ＧｕｏＤａｊｕｎ．ＰｅｒｏｄｉｃｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｓｅｃｏｎｄｏｒｄｅｒｉｍｐｕｌｓｉｖｅｉｎｔｅｇｒｏｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｉｎＢａｎａｃｈｓｐａｃｅ．ＮｏｎｌｉｎｅａｒＡｎａｌ，１９９７，２８：９８７－９９７
７　柴国庆．Ｂａｎａｃｈ空间非线性脉冲微分积分方程的极值解．数学物理学报，２０００，２０（１）：７４－８０

Initial Value Problems for Nonlinear Second Order Impulsive Integrodifferential Equations in Banach Space

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 1

Metrics

Comments

Recommended 10