Existence of multiple positive solutions for a third-order boundary value problem with nonlocal conditions

We study the existence of multiple positive solutions for a nonlinear third-order differential equation subject to various nonlocal boundary conditions. The boundary conditions that we study contain Stieltjes integral and include the special cases of m-point conditions and integral conditions. The main tool in the proof of our result is Krasnosel'skii's fixed point theorem. To illustrate the applicability of the obtained results, we consider examples.

Automated summary

This study investigates the existence of multiple positive solutions for a nonlinear third-order differential equation under various nonlocal boundary conditions. The boundary conditions examined include Stieltjes integral and special cases of m-point conditions and integral conditions. The main tool used in the proof is Krasnosel'skii's fixed point theorem. To demonstrate the applicability of the findings, examples are provided.