Existence of multiple positive solutions for a third-order boundary value problem with nonlocal conditions - Smirnov, Sergey (Nonlinear Analysis: Modelling and Control, 2023)
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.
Keywords: third-order nonlinear boundary value problems; nonlocal boundary conditions; existence of positive solutions; Green’s function; Krasnosel’skii’s fixed point theorem