  The aim of this work is to characterize the asymptotic behaviour of the first
eigenfunction of the generalised p-Laplace operator with mixed (Dirichlet and
Neumann) boundary conditions in cylindrical domains when the length of the
cylindrical domains tends to infinity. This generalises an earlier work of
Chipot et.al. "Asymptotics of eigenstates of elliptic problems with mixed
boundary data on domains tending to infinity" published in Asymptotic Analysis
in 2013, where the linear case p=2 is studied. Asymptotic behavior of all the
higher eigenvalues of the linear case and the second eigenvalues of general
case (using topological degree) for such problems is also studied.
