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, α > 1, β > 1, α + β∈(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 α > 1, β > 1, α + β ∈ (2,2*), and q is continuous and satisfies 0 < δ := infRN,g < supRN g =: γ < +∞, lim|x|→＋∞q(x) = γ.Then elliptic system(*) admits at least one nontrivia and nonnegative solution.