Positive solutions to a singular third-order three-point boundary value problem with an indefinitely signed Green’s function

Existence results of periodic solutions for third‐order nonlinear singular differential equation

“…At the beginning, most of work concentrated on second‐order singular differential equation, as in the references we mentioned above. Recently there have been published some results on third‐order singular differential equation (see 5, 13, 15, 17). For example, in 17, Sun investigated the three‐point boundary value problem By using Krasnosel'skii's fixed point theorem, he established the existence of single and multiple positive solutions to the boundary value problem.…”

Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems

“…By using the well-known Guo-Krasnoselskiȋ fixed point theorem [3], Palamides and Smyrlis [4] proved that there exists at least one positive solution for third-order three-point problem:…”

Positive solutions for a nonlinear third order multipoint boundary value problem

“…For example, Anderson [1998] established the existence of at least three positive solutions to the problem −x (t) + f (x(t)) = 0 for t ∈ (0, 1), x(0) = x (t 2 ) = x (1) = 0 for t 2 ∈ (0, 1), where f : R → [0, +∞) is continuous and 1/2 ≤ t 2 < 1. Palamides and Smyrlis [2008] proved that there exists at least one positive solution for the third order three-point BVP x (t) = a(t) f (t, x(t)) for t ∈ (0, 1),…”