一类奇异三阶三点边值问题的正解

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

中文关键词:  正解  奇异  三阶三点边值问题  不动点定理.

英文关键词:positive solutions  singular  third-order three-point BVP  fixed point theorem.

中文摘要:

      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.

英文摘要:

      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.