Resumen de Eigenvalue Problems of Ouasilinear Elliptic Systems on Rn.

Li Gongbao

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