Eigenvalue Problems of Quasilinear Elliptic Systems on $\mathbb R^n$

In this paper we get the existence results of the nontrivial weak solution (?,u) of the following eigenvalue problem of quasilinear elliptic systems-Da (aas(x,u) Dsui) + 1/2 Dui aas(x,u)Dauj Dsuj + h(x) ui = ?|u|p-2ui, for x I Rn, 1 = i = N and u = (u1, u2, ..., uN) I E = {v = (v1, v2, ..., vN) | vi I H1(Rn), 1 = i = N},where aas(x,u) satisfy the natural growth conditions. It seems that this kind of problem has never been dealt with before