Singularly perturbed elliptic problems with nonautonomous asymptotically   linear nonlinearities
  We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a saturation effect. We investigate the existence of nontrivial nonnegative solutions concentrating around local minima of both the potential and of the saturation function. Necessary conditions to locate the possible concentration points are also given. 
Liliane Maia, Eugenio Montefusco, Benedetta Pellacci
math.AP