Upper and Lower Solutions Method for First Order Impulsive Differential Equations with Integral Boundary Conditions
(1.College of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China;2.Department of Mathematics,Hunan Normal University,Changsha 410081,China)
Online:2007-03-25
Published:2012-06-18
About author:CHEN Guo-ping(1964-),male,was born in Shaoyang City,Hunan Province,associate professor of College of Mathematics and Computer Science,Ph. D of Hunan Normal University;research area is qualitaive theory of differential equations.
Supported by:
The NNSF of China (10571050)；Key Project of Hunan Province Education Department (03A023)
CHEN Guo-Ping, SHEN Jian-Hua. Upper and Lower Solutions Method for First Order Impulsive Differential Equations with Integral Boundary Conditions[J]. journal6, 2007, 28(2): 11-15.
[1] LAKSHNIKANTHAM V,BAINOV D D，SIMEONOV P S.Theory of Impulsive Differential Equations [M].Singapore:World Scientific,1989.[2] BAINOV D D，SIMEONOV P S.Syetems with Impulse Effect:Stability Theory and Applications [M].Chichester,Ellis Horwood 1989.[3] BAINOV D D，SIMEONOV P S.Impulsive Differential Equations:Periodic Solutions and Applications [M].Harlow:Longman Scientificand Technical,1993.[4] SHEN Jian-hua，LI Jian-li.Impulsive Control for Stability of Volterra Functional Differential Equations [J].Journal for Analysis and Its Applications,2005，24：721-734.[5] TADEUSZ JANKOWSKI.Differential Equations with Integral Boundary Conditions [J].Journal of Computational and Applied Mathematics,2002，147：1-8.[6] SAMOILENKO A M,MARTYNYUK S V.Justification of the Numerical-Analytic Method of Successive Approximations for Problems with Integral Boundary Conditions [J].Ukrain. Mat. Zh. SSR，1991，43：1 231-1 239.[7] LADDE G S,LAKSHMIKANTHAM V，VATSALA A S.Monotone Iterative Techniques for Nonlinear Differential Equations [M].Pitman,London,1985.[8] ZUO W,JIANG D,O’REGAN D,et al.Optimal Existence Conditions for the Periodic Delay j-Laplace Equation with Upper and Lower Solutions in the Reverse Order [J].Results Math.,2003，44：375-385.[9] HE Z，HE X.Monotone Iterative Technique for Impulsive Integro-Differential Equations with Periodic Boundary Conditions [J].Comput. Math. Appl.,2004,48：73-84.[10] RACHUNKOVA I,TVRDY M.Non-Order Lower and Upper Function in Second Order Impulsive Periodic Problems [J].Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal.,2005,12：397-415.
