Boundary Value Problems for Nonlinear Second Order Difference Equations With Impulse
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摘要: 研究二阶非线性脉冲微分方程边界值问题(BVPI).构造了BVPI的Green函数,并将非线性的BVPI转化为不动点问题,利用Banach不动点定理和Lipschitz条件,证明了该非线性BVPI解的唯一性,最后证明了BVPI解的存在性定理.Abstract: A boundary value problem with impulse (BVPI) for nonlinear second order difference equations is considered. Green's function of the BVPI was constructed and then the nonlinear BVPI was reduced to a fixed point problem. Banach fixed point theorem and Lipschitz condition were applied to show the uniqueness of solutions for the nonlinear BVPI. Finally, the theorem existence of solutions for the nonlinear BVPI was proved.
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Key words:
- impulse conditions /
- Green’s function /
- fixed point theorems /
- Lipschitz condition /
- existence /
- uniqueness
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[1] George R K,Nandakumaran A K,Arapostathis A. A note on controllability of impulsive systems[J].J Math Anal Appl,2000,241(2):276-283. doi: 10.1006/jmaa.1999.6632 [2] Guan Z H,Chen G,Ueta T.On impulsive control of a periodically forced chaotic pendulum system[J].IEEE Trans Automat Control,2000,45(9):1724-1727. doi: 10.1109/9.880633 [3] Nenov S.Impulsive controllability and optimization problems in population dynamics[J].Nonlinear Analysis:Theory,Methods Applications,1999,36(7):881-890. doi: 10.1016/S0362-546X(97)00627-5 [4] Lakmeche A,Arino O.Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment[J].Dynam Contin Discrete Impuls Systems,2000,7(2):265-287. [5] Lenci S,Rega G.Periodic solutions and bifurcations in an impact inverted pendulum under impulsive excitation[J].Chaos Solitons Fractals,2000,11(15):2453-2472. doi: 10.1016/S0960-0779(00)00030-8 [6] Bainov D D,Simeonov P S.Systems With Impulse Effects[M].Chichester:Ellis Horwood,1989. [7] Benchohra M,Henderson J,Ntouyas S.Impulsive Differential Equations and Inclusions[M].New York:Hindawi Publishing Corporation,2006. [8] Lakshmikantham V,Bainov D D,Simeonov P S.Theory of Impulsive Differential Equations[M]. Singapore:World Scientific,1989. [9] Samoilenko A M,Perestyuk N A.Impulsive Differential Equations[M].Singapore:World Scientific,1995. [10] Elaydi S N.An Introduction to Difference Equations[M].New York:Springer-Verlag,1996. [11] Kelley W G,Peterson A C.Difference Equations:An Introduction With Applications[M].New York:Academic Press,1991. [12] He Z M,Zhang X M.Monotone iterative technique for first order impulsive difference equations with periodic boundary conditions[J].Appl Math Comput,2004,156(3):605-620. doi: 10.1016/j.amc.2003.08.013 [13] LI Jian-li,SHEN Jian-hua.Positive solutions for first order difference equations with impulses[J].International Journal of Difference Equations,2006,1(2):225-239. [14] Tang X H,Yu J S.Oscillation and stability for a system of linear impulsive delay difference equations[J].Math Appl (Wuhan),2001,14:28-32. [15] Wang P,Wang W.Boundary value problems for first order impulsive difference equations[J].International Journal of Difference Equations,2006,1:249-259. [16] Zhang Q Q.On a linear delay difference equation with impulses[J].Ann Differential Equations,2002,18(2):197-204. [17] Bereketoglu H,Huseynov A.On positive solutions for a nonlinear boundary value problem with impulse[J].Czechoslovak Mathematical Journal,2006,56(1):247-265. doi: 10.1007/s10587-006-0015-7
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