Entire Solutions for a Quasilinear Problem in the Presence of Sublinear and Super-Linear Terms

We establish new results concerning existence and asymptotic behavior of entire, positive, and bounded solutions which converge to zero at infinite for the quasilinear equation Δpu=a(x)f(u)+λb(x)g(u), x∈ N, 10. Penalty arguments, variational principles, lower-upper solutions, and an approximation procedure will be explored.