Infinitely many solutions for a fourth-order boundary-value problem

In this article we consider the existence of infinitely many solutions to the fourth-order boundary-value problem $$displaylines{ u^{iv}+alpha u''+eta(x) u=lambda f(x,u)+h(u),quad xin]0,1[cr u(0)=u(1)=0,cr u''(0)=u''(1)=0,. }$$ Our approach is based on variational methods and critical point theory.