The Existence Of Solutions For A Polyharmonic Equation Involving Critical Exponent

In this paper,we study the following polyharmonic equation involving critical Sobolev exponent(?) where m?N+,N>2m+1,2*=2N/N-2m,g(x,u)=h(x)|u|q-1u(1<q<2*-1),g(x,u)=K(x)|u|2*-2u+b(x)u or g(x,u)=K(|x|)|u|2*-2u.By using perturbation method and reduction method,we transform the existence of critical point of energy functional in infinite dimensional space into the existence of critical point of pertur-bation term in finite dimensional space.Under some conditions on K and h,we prove that there exists an ?0>0 such that this equation has a nontrivial solution for all? ?(-?0,?0).