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

## Main Article Content

## Abstract

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.

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## References

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