Electron. J. Diff. Equ., Vol. 2012 (2012), No. 164, pp. 1-14.

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

Seyyed Mohsen Khalkhali, Shapour Heidarkhani, Abdolrahman Razani

In this article we consider the existence of infinitely many solutions to the fourth-order boundary-value problem
  u^{iv}+\alpha u''+\beta(x) u=\lambda f(x,u)+h(u),\quad x\in]0,1[\cr
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.

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Seyyed Mohsen Khalkhali
Department of Mathematics, Science and Research branch
Islamic Azad University, Tehran, Iran
email: sm.khalkhali@srbiau.ac.ir
Shapour Heidarkhani
Department of Mathematics, Faculty of Sciences
Razi University, 67149 Kermanshah, Iran
email: sh.heidarkhani@yahoo.com, s.heidarkhani@razi.ac.ir
Abdolrahman Razani
Department of Mathematics, Science and Research Branch
Islamic Azad University, Tehran, Iran.
School of Mathematics
Institute for Research in Fundamental Sciences
P.O. Box 19395-5746, Tehran, Iran
email: razani@ikiu.ac.ir

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