摘要:
运用上下解的单调迭代方法讨论三阶常微分方程边值问题{-u'''(t)=f(t,u(t),u'(t)),t∈[0,1]/u(0)=u'(0)=u'(1)=0解的存在性,其中f(t,u,v):[0,1]×R×R→R为连续函数.在f关于u,v满足较弱单调条件的情形下,建立了一个新的极大值原理,并利用其获得了上述边值问题解的存在性结果.
Abstract:
In this paper, by using the monotone iterative method we discuss the existence of the solutions for the third-order boundary value problem {-u'''(t)=f(t,u(t),u'(t)),t∈[0,1]/u(0)=u'(0)=u'(1) = 0 where f(t,u,v):[0,1]×R×R→R is continuous. If f satisfies weaker monotone conditions about u and v, the authors establish a new maximum principle and obtain the existence results of the solutions.
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