Abstract
We establish new results concerning the existence and asymptotic behaviour of solutions for the nonlinear elliptic problem where Δ p u = div(|∇u| p−2∇u), with 1 < p < N, denotes the p-Laplacian operator and f : ℝ N × (0, ∞) → ℝ is a suitable continuous function. The principal aim of this article is to study the case 0 < l < ∞, because the extreme cases l = 0 and l = ∞ have been intensely studied in recent years. The main tools we use to prove the principal results are the method of lower and upper solutions, an argument of penalization and a technique of monotonization–regularization of the nonlinearity f.
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