Bubbling solutions for an anisotropic planar elliptic problem with exponential nonlinearity

Let Ω be a bounded domain in R2 with smooth boundary, we study the following anisotropic elliptic problem −∇(a(x)∇υ)=a(x)[eυ−sϕ1−h(x)]inΩ,υ=0on∂Ω,where a(x) is a positive smooth function, h∈C0,α(Ω¯), s>0 is a large parameter and ϕ1 is a positive first eigenfunction of the problem −∇(a(x)∇ϕ)=λa(x)ϕ under Dirichlet boundary condition in Ω. We construct solutions of this problem which exhibit multiple concentration behavior around maximum points of a(x)ϕ1 in the domain as s→+∞.