No abstract

In this paper, we develop criteria for the existence of multiple positive solutions for second order Sturm-Liouville boundary value problem,where k ∈ 0, π 2 is a constant, by an application of Avery-Henderson fixed point theorem.

In this paper, we consider the second-order differential equations of the form [Formula: see text] satisfying the Sturm–Liouville boundary conditions [Formula: see text] where [Formula: see text]. By an application of Avery–Henderson fixed point theorem, we establish conditions for the existence of multiple positive solutions to the boundary value problem.

We investigate the eigenvalue intervals of [Formula: see text] for which the iterative system of four-point fractional-order boundary value problem has at least one positive solution by utilizing Guo–Krasnosel’skii fixed point theorem under suitable conditions. The obtained results in the paper are illustrated with an example for their feasibility.