THE PROOF OF THE EXISTENCE OF THE THIRD SOLUTION OF A NONLINEAR BIHARMONIC EQUATION BY DEGREE THEORY

We investigate the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition,${\Delta}^2u+c{\Delta}u=bu^{+}+s$, in ­${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show by degree theory that there exist at least three solutions of the problem.