Superlinear Equations Involving Nonlinearities Limited by Asymptotically Homogeneous Functions

Abstract

We obtain a solution of the quasilinear equation −Δpu=f(u) in Ω, u=0, on ∂Ω. Here the nonlinearity f is superlinear at zero, and it is located near infinity between two functions that belong to a class of functions where the Ambrosetti-Rabinowitz condition is satisfied. More precisely, we consider the class of functions that are asymptotically homogeneous of index q.