Global structure of positive solutions for some second-order multipoint boundary value problems
Summary: We investigate in this paper the following second-order multipoint boundary value problem: \[ \begin{aligned} -(L\varphi)(t)=\lambda f(t,\varphi(t)), \quad 0\leq t\leq 1, \\ \varphi^\prime(0)=0, \quad\varphi (1)=\sum_{i=1}^{m-2}\beta_i \varphi (\eta_i). \end{aligned} \] Under some conditions, we obtain the global structure of the positive solution set of this boundary value problem and the behavior of positive solutions with respect to the parameter \(\lambda\) by using the global bifurcation method. We also obtain the infinite interval of the parameter \(\lambda\) about the existence of positive solutions.
scientific article; zbMATH DE number 6801990
scientific article