Existence and multiplicity of solutions of a kind of fourth-order boundary value problem

In this paper, the existence and multiplicity results of the solutions are obtained for the fourth-order boundary value problem u(4)(t)=f(t,u(t)) for all t∈[0,1] subject to u(0)=u(1)=u″(0)=u″(1)=0, where f is continuous. The monotone operator theory and critical point theory are employed to discuss this problem, respectively.