The Existence of two Positive Solutions to Three-point Boundary Value Problem on Time Scales
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摘要: 运用锥上的Avery-Henderson不动点定理，研究了时间测度链上一类非线性3点边值问题 至少2个正解的存在性, 其中, 表示时间测度链, , .并给出了与之相对应的线性３点边值问题解的一些性质,举例证明了所得结论的正确性.
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关键词:
- 正解
Abstract: Existence of at least two positive solutions to a nonlinear three-point boundary value problem on time scales is considered, and the main tool is well-known Avery-Henderson fixed-point theorem in cones. The solution and some of its properties of the linear three-point boundary value problem related to the nonlinear boundary value problem are provided. At last, an example is given to demonstrate the result of this study.-
Keywords:
- positive solution
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[1]Hilger S.Analysis on measure chains: A unified approach to continuous and discrete calculusResults Math. 1990,18:18-56.[J].Results Math, 1990, 18(1):18-56 [2]Agarwal R.P., Bohner M., Li W. T., Nonoscillation and oscillation theory for functional differential equations, pure and applied mathematics series[M]. New York: Marcel Dekker, 2004. [3]Bohner M.Peterson A., Dynamic Equations on Time scales, an Introduction with Applications[M].Boston: [4]Sun J.P.,Perera K,Existence of positive solution to second-order three-point BVPs on time scales[J].Boundary Value Problems 2009, 2009(1):10-15.[J].Boundary Value Problems, 2009, 2009(1):10-15 [5]Agarwal R.P.,Bohner M,Saker SH.,Oscillation of second order delay dynamic equations[J].Canadian Applied Mathematics Quarterly, 2005, 13(1):1-18 [6]Liang G.H.,Xian FZ.,Positive solutions of semipositone higher-order differential equations on time scales[J].Nonlinear Analysis 2011, 74(9):3033-3045.[J].Nonlinear Analysis, 2011, 74(9):3033-3045 [7]Kameswara A.R.,Positive solution for a system of nonlinear boundary-value problem on time scalesElectron. J.Diff.Equ.,Anal.2009,127(1):1-9.[J].Electron. J.Diff.Equ., Anal, 2009, 127(1):1-9 [8]Zhao J.F.,Lian HR.,Ge. W. G.,Existence of positive solutions for nonlinear m-point boundary problems on time scales[J].Boundary Value Problems 2012, 2012(1):1-15.[J].Boundary Value Problems, 2012, 2012(1):1-15 [9]Avery M.A.,Henderson J,Two positive fixed points of nonlinear operators on ordered Banach spaces,Comm. Appl. Nonlinear Anal. 8(2001)：27-36.[J].Comm. Appl. Nonlinear Anal., 2002, 2001(8):27-36 [1]Hilger S.Analysis on measure chains: A unified approach to continuous and discrete calculusResults Math. 1990,18:18-56.[J].Results Math, 1990, 18(1):18-56 [2]Agarwal R.P., Bohner M., Li W. T., Nonoscillation and oscillation theory for functional differential equations, pure and applied mathematics series[M]. New York: Marcel Dekker, 2004. [3]Bohner M.Peterson A., Dynamic Equations on Time scales, an Introduction with Applications[M].Boston: [4]Sun J.P.,Perera K,Existence of positive solution to second-order three-point BVPs on time scales[J].Boundary Value Problems 2009, 2009(1):10-15.[J].Boundary Value Problems, 2009, 2009(1):10-15 [5]Agarwal R.P.,Bohner M,Saker SH.,Oscillation of second order delay dynamic equations[J].Canadian Applied Mathematics Quarterly, 2005, 13(1):1-18 [6]Liang G.H.,Xian FZ.,Positive solutions of semipositone higher-order differential equations on time scales[J].Nonlinear Analysis 2011, 74(9):3033-3045.[J].Nonlinear Analysis, 2011, 74(9):3033-3045 [7]Kameswara A.R.,Positive solution for a system of nonlinear boundary-value problem on time scalesElectron. J.Diff.Equ.,Anal.2009,127(1):1-9.[J].Electron. J.Diff.Equ., Anal, 2009, 127(1):1-9 [8]Zhao J.F.,Lian HR.,Ge. W. G.,Existence of positive solutions for nonlinear m-point boundary problems on time scales[J].Boundary Value Problems 2012, 2012(1):1-15.[J].Boundary Value Problems, 2012, 2012(1):1-15 [9]Avery M.A.,Henderson J,Two positive fixed points of nonlinear operators on ordered Banach spaces,Comm. Appl. Nonlinear Anal. 8(2001)：27-36.[J].Comm. Appl. Nonlinear Anal., 2002, 2001(8):27-36
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