On the Existence and Nonexistence of Positive Solutions for Singular Quasilinear Elliptic Equations with Gradient Terms

In this paper, we investigate the positive solutions of quasilinear elliptic equations of the form−∆pu=a(δ(x))g(u) +f(x,u) +λ|∇u|p−1,inBRu >0,inBRu= 0,on∂BR(1.1)whereBR(0)⊂RN,N≥2is an open ball centered at origin ofRN,gis an unbounded decreasingfunction,a(δ(x))is positive and continuous,δ(x) =dist(x,∂BR),p≥2,λ <0. We emphasis theeffect of all these terms in the study of existence and nonexistence of positive solutions.