MULTIPLICITY RESULTS ON A NONLINEAR BIHARMONIC EQUATION

Let Omega be a bounded open set in R-n with smooth boundary partial de rivative Omega. We are concerned with a fourth order semilinear ellipt ic boundary value problem Delta(2)u + c Delta u = bu(+) + s in Omega u nder Dirichlet boundary condition. We investigate the existence of sol utions of the fourth order nonlinear equation (0.1) when the nonlinear ity bu(+) crosses eigenvalues of Delta(2) + c Delta under Dirichlet bo undary condition.