  We analyze the asymptotic behavior of the eigenvalues of nonlinear elliptic
problems under Dirichlet boundary conditions and mixed (Dirichlet, Neumann)
boundary conditions on domains becoming unbounded. We make intensive use of
Picone identity to overcome nonlinearity complications. Altogether the use of
Picone identity makes the proof easier with respect to the known proof in the
linear case. Surprisingly the asymptotic behavior under mixed boundary
conditions critically differs from the case of pure Dirichlet boundary
conditions for some class of problems.
