Korean J. Math. Vol. 22 No. 4 (2014) pp.633-644
DOI: https://doi.org/10.11568/kjm.2014.22.4.633

# At least two solutions for the semilinear biharmonic boundary value problem

## Abstract

We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when
the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle.
We also get another theorem that there exist at least two solutions when there exist $n$ eigenvalues
of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0.
We prove this result by the critical point theory and the variation of linking method.

## Supporting Agencies

This work was supported by Basic Science Research Program through the Na- tional Research Foundation of Korea(NRF) funded by the Ministry of Education Science and Technology (KRF-2013010343).

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