Multiple Solutions Of Navier Boundary Value Problem For A Biharmonic Equation With Constraint

This dissertation deals with the existence of multiple solutions of the biharmonic equation with constraint(?)under the Navier boundary condition:u|(?)?=?u|(?)?=0,where ?(?)RN(N>4)is a bounded domain with smooth boundary(?)?.The dissertation is divided into two parts.In the first part,we proved that the above equation has a positive solution and a negative one,under some appropriate assumptions on f using the variational method.We also proved the existence of a third solution,which is sign-changing by using the descending flow method.In the second part,under a stronger assumption on f,we also proved the existence of a positive solution,a negative solution and a sign-changing one of the above equation by using decomposition in dual cones.