Nontrivial solutions for some fourth order boundary value problems with parameters

In this paper, we prove some new existence results concerning nontrivial solutions to some fourth order boundary value problems u(4)(t)+ηu″(t)−ξu(t)=f(t,u(t))u(4)(t)+ηu″(t)−ξu(t)=f(t,u(t)), 0