In this article we consider the existence of infinitely many solutions to the fourth-order boundary-value problem
![$$\displaylines{
u^{iv}+\alpha u''+\beta(x) u=\lambda f(x,u)+h(u),\quad x\in]0,1[\cr
u(0)=u(1)=0,\cr
u''(0)=u''(1)=0\,.
}$$](gifs/aa.gif)
Our approach is based on variational methods and critical point theory.
Seyyed Mohsen Khalkhali, Shapour Heidarkhani, Abdolrahman Razani
Abstract:
In this article we consider the existence of infinitely many
solutions to the fourth-order boundary-value problem
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 |
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Shapour Heidarkhani Department of Mathematics, Faculty of Sciences Razi University, 67149 Kermanshah, Iran email: sh.heidarkhani@yahoo.com, s.heidarkhani@razi.ac.ir |
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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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