Concentration solutions to the singularly prescribed Gaussian and geodesic curvatures problem

We consider the following Liouville-type equation with exponential Neumann boundary condition: [Formula presented] where D⊂R² is the unit disk, ε²K(x)>0 and εκ(x)>0 stand for the prescribed Gaussian curvature and geodesic curvature of the boundary, respectively. We prove the existence of concentration solutions if κ(x)+K(x)+κ(x)² (x∈∂D) has a local extremum point, which is a new result for exponential Neumann boundary problems.