Electron. J. Diff. Equ., Vol. 2012 (2012), No. 84, pp. 1-15.

Existence of solutions for a two-point boundary-value problem of a fourth-order Sturm-Liouville type

Shapour Heidarkhani

In this work, we establish the existence of two intervals for a parameter $\lambda$ for which a two-point boundary-value problem of fourth-order Sturm-Liouville type admits three weak solutions whose norms are uniformly bounded with respect to $\lambda$. Employing two three critical point theorems, existence of at least three weak solutions is ensured. This approach is based on variational methods and critical point theory.

Submitted January 20, 2012. Published May 23, 2012.
Math Subject Classifications: 35J35, 47J10, 58E05.
Key Words: Fourth-order Sturm-Liouville problem; critical point; multiplicity of solutions.

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Shapour Heidarkhani
Department of Mathematics, Faculty of Sciences
Razi University, 67149 Kermanshah, Iran
School of Mathematics
Institute for Research in Fundamental Sciences
P.O. Box 19395-5746, Tehran, Iran
email: sh.heidarkhani@yahoo.com   s.heidarkhani@razi.ac.ir

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