Singular limits solution for two-dimensional elliptic problems involving exponential nonlinearities with nonlinear gradient terms and singular weights

Given Ω bounded open regular set of ${mathbb{R}^2}$ , ${q_1,ldots, q_K in Omega}$ , ${varrho : Omega longrightarrow [0,+infty)}$ a regular bounded function and ${V: Omega longrightarrow [0,+infty)}$ a bounded fuction. We give a sufficient condition for the model problem $$(P):qquad-{Delta}u -{lambda}varrho(x)|{nabla}u|^2 = varepsilon^{2}V(x)e^u$$ to have a positive weak solution in Ω with u = 0 on ?Ω, which is singular at each q _i as the parameters ${varepsilon}$ and λ tend to 0, essentially when the set of concentration points q _i and the set of zeros of V are not necessarily disjoint.