Existence Of Solutions For Elliptic System In The Whole Space

In this paper, we study the following elliptic system:where N? 3, q is continuous, ? > 1, ? > 1, ? + ??(2, 2*), where 2* denotes the critical Sobolev exponent, that is 2* =N/N-2.We use the variational method to prove the conclusion as follows:Theorem Assumc that ? > 1, ? > 1, ? + ? ? (2,2*), and q is continuous and satisfies 0 < ? := infRN,g < supRN g =: ? < +?, lim|x|???q(x) = ?.Then elliptic system(*) admits at least one nontrivia and nonnegative solution.