Positive Solution of Fourth-Order Integral Boundary Value Problem with Two Parameters

The author investigates the fourth-order integral boundary value problem with two parameters u(4)(t)+βu′′(t)-αu(t)=f(t,u),t∈(0,1),  u(0)=u(1)=0,  u′′(0)=∫01u(s)ϕ1(s)ds,u′′(1)=∫01u(s)ϕ2(s)ds, where nonlinear term function f is allowed to change sign. Applying the fixed point index theorem on cone together with the operator spectrum theorem, some results on the existence of positive solution are obtained