Existence of Positive Solutions for Second-Order Third-Point Semipositive BVP

Abstract

In this paper, we study the existence of positive solutions for the following nonlinear second-order third-point semi-positive BVP. We derive an explicit interval of positive parameters, which for any $l,\mu$ in this interval, the existence of positive solutions to the boundary value problem is guaranteed under the condition that $a\left(t,x\right),b\left(t,x\right)$ are all superlinear (sublinear), or one is superlinear, the other is sublinear.