Concave-convex effects for critical quasilinear elliptic problems
  It is established existence, multiplicity and asymptotic behavior of positive solutions for a quasilinear elliptic problem driven by the $\Phi$-Laplacian operator. One of these solutions is obtained as ground state solution by applying the well known Nehari method. The semilinear term in the quasilinear equation is a concave-convex function which presents a critical behavior at infinity. The concentration compactness principle is used in order to recover the compactness required in variational methods. 
C. Goulart, E. D. da Silva, M. L. M. Carvalho, J. V. Goncalves
math.AP