The Existence Of Three Critical Points Of A Class Of Nonlinear Functionals On W^{1, P}(R^N)

In this paper, we consider the existence of three critical points for the nonlinear functional:defined on W_r^1,p(R^N). This nonlinear functional originates from the nonlinear elliptic equation:where 10(R¹,R¹) satisfies the sublinear growth condition. We apply a Three Critical Point Theorem defined by G.Bonanno (in [3]) to prove that the nonlinear functional Iλ(u) has at least three critical points in W_r^1,p(R^N).Ifp=2, we prove that the nonlinear functional Iλ(u) has at least three critical points in W^1,2(R^N) .