姚庆六. 一类非线性三阶两点边值问题的单调迭代方法[J]. 云南大学学报(自然科学版), 2011, 33(1): 1-5,10 .
引用本文: 姚庆六. 一类非线性三阶两点边值问题的单调迭代方法[J]. 云南大学学报(自然科学版), 2011, 33(1): 1-5,10 .
YAO Qing-liu. Monotonic iteration method to a nonlinear third-order two-point boundary value problem[J]. Journal of Yunnan University: Natural Sciences Edition, 2011, 33(1): 1-5,10 .
Citation: YAO Qing-liu. Monotonic iteration method to a nonlinear third-order two-point boundary value problem[J]. Journal of Yunnan University: Natural Sciences Edition, 2011, 33(1): 1-5,10 .

一类非线性三阶两点边值问题的单调迭代方法

Monotonic iteration method to a nonlinear third-order two-point boundary value problem

  • 摘要: 研究了一类非线性三阶两点边值问题非平凡解的单调迭代方法,其中非线性项包含了未知函数的一、二阶导数并且可以改变符号.利用Green函数此问题被转化为一个积分方程.通过构造2个单调迭代序列并且考察这些序列的收敛性证明了相伴积分算子具有非0不动点.进而证明了这个三阶两点边值问题非平凡解的存在性.

     

    Abstract: The monotonic iteration method of nontrivial solutions is studied for a nonlinear third-order two-point boundary value problem in which the nonlinear term contains first and second derivatives of unknown function and may change sign.By applying Green function the problem is transformed into an integral equation.By constructing two monotonically iterative sequences and considering the convergence of these sequences,the existence of nonzero fixed points is proved for the associated integral operator.Further,the existence of nontrivial solutions is verified for the third-order two-point boundary value problem.

     

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