Bifurcation and asymptotical behavior for singular elliptic equation with a linear convection term

We examine the elliptic equation −Δu=p(R−|x|)g(u)+f(x,u)+μ|∇u|−Δu=p(R−|x|)g(u)+f(x,u)+μ|∇u|, in BRBR, u=0u=0, on ∂BR∂BR, where μ∈Rμ∈R, ff is a nondecreasing function with sublinear growth, pp is a singular positive weight and gg is decreasing and unbounded around the origin. We establish the existence of positive solution for all μ∈Rμ∈R and describe the precise asymptotical behavior of the solution near boundary.