Positive Solutions to a Singular Third-Order Three-Point Boundary Value Problem

DOI：10.3770/j.issn:1000-341X.2011.02.012

 作者 单位 吴红萍 西北师范大学数学与信息科学学院, 甘肃 兰州 730070

本文利用锥上的不动点定理,研究奇异三阶三点边值问题$\left\{\begin{array}{lcr}u'''(t)=-\lambda a(t)f(t,u(t))\\u(0)=u'(1)=u''(\eta)=0\end{array}\right.$正解的存在性,其中$\lambda>0$,得到了正解存在的若干新结果,这些正解是严格增的,并给出了一个实例.

In this paper, we study the existence of positive solutions for the nonlinear singular third-order three-point boundary value problem $$\left\{\begin{array}{l}u'''(t)=-\lambda a(t)f(t,u(t)),\\ u(0)=u'(1)=u''(\eta)=0,\end{array}\right.$$ where $\lambda$ is a positive parameter and $0\le\eta<\frac{1}{2}$. By using the classical Krasnosel'skii's fixed point theorem in cone, we obtain various new results on the existence of positive solution, and the solution is strictly increasing. Finally we give an example.