On A Class Of Singular Elliptic Problems With First Order Terms

This paper is concerned with the existence and the nonexistence of solutions to semi-linear elliptic problems of the following type:where Ω(?)R~n(n> 3) will be either R~n, or a bounded open set with smooth boundary,which contains the origin, A, a are real parameters, f ∈ C(R~+, R~+). Under suitable assumptions, we prove the existence of nontrivial weak solutions to the problems in the region {(a, λ) : 2 — n < λ < λ — 2a/q-2} and the nonexistence of local nontrivial weak solutions (or very nontrivial weak solutions)to the problems in the region {(a, λ) : a ≥ 2, λ > λ — a/q-2} by mountain pass lemma and Pohozaev identity. Moreover, the existence of nontrivialradial solutions to the problems in the region {(a, λ) : λ< 2 - n, λ < λ-a/q-2} isalso obtained,where q is a constant depending on f, λ =2n-qn+2q/q-2,λ=λ-2/q-2.Thus we expanded most of the conclusions in the paper "Advances in Differential Equations 8(2003)".