Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation

The authors investigate relations between multiplicity of solutions and source terms of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition Delta(2)u + c Delta u = bu(+) + f in Omega, where Omega is a bounded open set in R-n with smooth boundary and the nonlinearity bu(+) crosses eigenvalues of Delta(2) + c Delta. They investigate the relations when the source term is constant and when it is generated by two eigenfunctions.