应用数学学报 2012, Vol. Issue (4): 737-746    DOI:
 论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索  |  Existence Theorems of Positive Solution to a Nonlinear Cantilever Beam Equation
YAO Qingliu
Department of Applied Mathematics, Nanjing University ofFinance and Economics, Nanjing 210003
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u(4)(t)=f(t,u(t),u'(t)), 0<t<1, u(0)=u'(0)=u''(1)=u'''(1)=0

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Abstract： The positive solution is studied for the nonlinear cantilever beam equation
u(4)(t)=f(t,u(t),u'(t)), 0≤ t ≤1, u(0)=u'(0)=u''(1)=u'''(1)=0,
where the nonlinear term f(t,u,v) may be singular at t=0, t=1. By making use of Krasnosel'skii fixed point theorem in degree theory and Lebesgue dominated convergence theorem and Fatou lemma in real variable, two new existence theorems of positive solution are proved when there are growth limit functions.

 引用本文: 姚庆六. 非线性悬臂梁方程的正解存在定理[J]. 应用数学学报, 2012, (4): 737-746. YAO Qingliu. Existence Theorems of Positive Solution to a Nonlinear Cantilever Beam Equation[J]. Acta Mathematicae Applicatae Sinica, 2012, (4): 737-746.

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