Multiple blow-up solutions for an exponential nonlinearity with potential in R2R2

We study the following boundary value problem equation(0.1){Δu+λa(x)up−1eup=0,u>0inΩ;u=0on∂Ω, where ΩΩ is a bounded domain in R2R2 with smooth boundary, λ>0λ>0 is a small parameter, the function a(x)≥0a(x)≥0 is a smooth potential, and the exponent pp satisfies 0