Existence of positive solutions for a class of second-order two-point boundary value problem

Abstract

By using different convex functionals to compute fixed point index, the existence of positive solutions for a class of second-order two-point boundary value problem $$\left\{\begin{array}{l} \varphi^{\prime\prime}(t) + h(t)f(\varphi(t)) = 0,\,\, 0 < t < 1,\\ \alpha\varphi(0) - \beta\varphi^{\prime}(0) = 0,\,\, \gamma\varphi(1) + \delta\varphi^{\prime}(1) = 0, \end{array}\right.$$ is obtained under some conditions of growth, where α, β, γ, δ ≥ 0, ρ = αγ + γβ + δα > 0, and h(t) is allowed to be singular at t = 0 and t = 1.