一类非线性三点本征值问题的正解
Positive solutions of a nonlinear three-point eigenvalue problem with integral boundary conditions
摘要：
本文研究了二阶微分方程\begin{equation*} \begin{gathered} {u^{\prime \prime }}(t)+λa(t)f(u(t))=0,\ \ 0<t<1, \\ u^{\prime}(0)=0, \ u(1)=α\int_{0}^ηu(s)ds, \end{gathered} \end{equation*}的三点积分边值问题正解的存在性，其中$λ>0$是参数，$0<η<1$，$0<α< \frac{1}{η}$ .利用Green函数的性质和锥上的Krasnoselskii不动点定理，研究了一类非线性边值问题的特征值区间，建立了至少存在一个正解的充分条件.
英文摘要：
In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP) for the following second-order differential equation \begin{equation*} \begin{gathered} {u^{\prime \prime }}(t)+λa(t)f(u(t))=0,\ \ 0<t<1, \\ u^{\prime}(0)=0, \ u(1)=α\int_{0}^ηu(s)ds, \end{gathered} \end{equation*} where $λ>0$ is a parameter, $0<η<1$, $0<α< \frac{1}{η}$. By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
