Positive Solutions of Three-Order Delayed Periodic Boundary Value Problems

Abstract EN

Our main purpose is to consider the existence of positive solutions for three-order two-point boundary value problem in the following form: u′′′(t)+ρ3u(t)=f(t,u(t-τ)), 0≤t≤2π, u(i)(0)=u(i)(2π), i=1,2, u(t)=σ, -τ≤t≤0, where σ,ρ, and τ are given constants satisfying τ∈(0,π/2).

Some inequality conditions on ρ3u-f(t,u) guaranteeing the existence and nonexistence of positive solutions are presented.

Our discussion is based on the fixed point theorem in cones.