Bifurcation For Singular P-Laplacian Problems With Convection Term

In this paper,we study the bifurcation problem whereλ,μ≥0,andΩis bounded domain in RN.The singular character of the problem is given by the nonlinearity g which is assumed to be strictly decreasing and unbounded around the origin.We use the skill to eliminate the conviction term and combine the maxmium principle and the Picone's identity for the p-Laplacian to prove that the above problem has a positive solution(which is unique)ifλ(α+μ)<λ1；it has no positive solution ifλ(α+μ)≥λ1,whereα=limt→∞g(t)andλ1 is the first eigenvalue of—Δp in W01,p(Ω).