Positive Solutions for(n-1,1) m-Point Boundary Value Problems With Dependence on the First Order Derivative
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摘要: 利用锥上的Krasnoselskii's不动点定理的推广定理,讨论了一类边值问题,给出了相应依赖于一阶导数的非线性n阶m点边值问题至少一个正解的存在性.对于n阶m点边值问题,给出了相应的Green函数,证明了在非线性项f满足一定的增长条件下至少存在1个正解.并且给出了一个例子来说明所获得的结果.Abstract: Using the extension of Krasnoselskii's fixed point theorem in a cone,the existence of at least one positive solution to the nonlinear n th order m-point boundary value problem with dependence on the first order derivative was proved.The associated Green's function for the n th order mpoint boundary value problem was given,and growth conditions were imposed on nonlinear term f which ensure existence of at least one positive solutions.A simple example was presented to illustrate applications of the obtained results.
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[1] l'in V A,Moiseev E I.Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator[J].Differential Equations,1987,23(8):979-987. [1] l'in V A,Moiseev E I.Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects[J].Differential Equations,1987,23(7):803-810. [3] MA Ru-yun. Positive solutions of a nonlinear three-point boundary value problems[J]. Electronic Journal of Differential Equations,1999,34(4):1-8. [4] MA Ru-yun. Existence theorems for a second order m-point boundary value problems[J]. J Math Anal Appl,1997,211(2):545-555. doi: 10.1006/jmaa.1997.5416 [5] MA Ru-yun. Positive solutions for second order three-point boundary value problems[J]. Applied Mathematics Letters,2001,14(1):1-5. doi: 10.1016/S0893-9659(00)00102-6 [6] MA Ru-yun. Existence theorems for a second order three-point boundary value problems[J]. J Math Anal Appl,1997,212(2):430-442. doi: 10.1006/jmaa.1997.5515 [7] LIU Xiu-jun,QIU Ji-qing,GUO Yan-ping. Three positive solutions for second-order m-point boundary value problems[J]. Applied Mathematics and Computation,2004,156(3):733-742. doi: 10.1016/j.amc.2003.06.021 [8] GUO Yan-ping,SHAN Wen-rui,GE Wei-gao. Positive solutions for second-order m-point boundary value problems[J]. Journal of Computational and Applied Mathematics,2003,151(2):415-424. doi: 10.1016/S0377-0427(02)00739-2 [9] GUO Yan-ping,GE Wei-gao.Positive solutions for three-point boundary value problems with dependence on the first order derivatives[J]. J Math Anal Appl,2004,290(1):291-301. doi: 10.1016/j.jmaa.2003.09.061 [10] Eloe Paul W,Ahmad Bashir. Positive solutions of a nonlinear nth boundary value problems with nonlocal conditions[J]. Applied Mathematics Letters,2005,18(5):521-527. doi: 10.1016/j.aml.2004.05.009 [11] Eloe Paul W,Henderson Johnny. Positive solutions for (n-1,1) conjugate boundary value problems[J].Nonlinear Anal,1997,28(10):1669-1680. doi: 10.1016/0362-546X(95)00238-Q
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