Multiplicity results on a nonlinear biharmonic equation Original Research Article

Let ω be a bounded open set in Rn with smooth boundary ϖω We are concerned with a fourth order semilinear elliptic boundary value problem Δ2u + cΔu = bu+ + s inω under Dirichlet boundary condition. We investigate the existence of solutions of the fourth order nonlinear equation (0.1) when the nonlinearity bu+ crosses eigenvalues of Δ2 + cΔ under Dirichlet boundary condition.