In this paper, we consider the following fourth order ordinary differential equation x(4)(t) = f(t,x(t),x (t),x (t),x (t)), t ∈ (0,1) (E) with the four-point boundary value conditions: x(0) = x(1) = 0, αx (ξ1) - β...In this paper, we consider the following fourth order ordinary differential equation x(4)(t) = f(t,x(t),x (t),x (t),x (t)), t ∈ (0,1) (E) with the four-point boundary value conditions: x(0) = x(1) = 0, αx (ξ1) - βx (ξ1) = 0, γx (ξ2) + δx (ξ2) = 0, (B) where 0 < ξ1 < ξ2 < 1. At the resonance condition αδ + βγ + αγ(ξ2 - ξ1) = 0, an existence result is given by using the coincidence degree theory. We also give an example to demonstrate the result.展开更多
基金the Master’s Research Fund of Suzhou University (No.2008yss19)
文摘In this paper, we consider the following fourth order ordinary differential equation x(4)(t) = f(t,x(t),x (t),x (t),x (t)), t ∈ (0,1) (E) with the four-point boundary value conditions: x(0) = x(1) = 0, αx (ξ1) - βx (ξ1) = 0, γx (ξ2) + δx (ξ2) = 0, (B) where 0 < ξ1 < ξ2 < 1. At the resonance condition αδ + βγ + αγ(ξ2 - ξ1) = 0, an existence result is given by using the coincidence degree theory. We also give an example to demonstrate the result.
