Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions

Abstract EN

We consider the following third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions: u ′ ′ ′ t + f t , u α t = 0 , t ∈ 0 , 1 , u 0 = γ u η 1 + λ 1 u and u ′ ′ 0 = 0 , u 1 = β u η 2 + λ 2 u , where 0 < η 1 < η 2 < 1 , 0 ≤ γ , β ≤ 1 , α : [ 0,1 ] → [ 0,1 ] is continuous, α ( t ) ≥ t for t ∈ [ 0,1 ] , and α ( t ) ≤ η 2 for t ∈ [ η 1 , η 2 ] .

Under some suitable conditions, by applying a fixed point theorem due to Avery and Peterson, we obtain the existence of multiple positive solutions to the above problem.

An example is also included to illustrate the main results obtained.