Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 164, pp. 1-14.

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

Authors: Seyyed Mohsen Khalkhali (Islamic Azad Univ., Tehran, Iran)
         Shapour Heidarkhani  (Razi Univ., Kermanshah, Iran)
	 Abdolrahman Razani(Islamic Azad Univ., Tehran, Iran)

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

Submitted June 28, 2012 Published September 22, 2012.
Math Subject Classifications: 34B15.
Key Words: Fourth-order equation; infinitely many solutions; 
           critical point theory; variational methods.