Abstract
In this paper we deal with the following quasilinear elliptic problems
where Ω ⊂ ℝN is a bounded regular domain, d(x) = dist(x, ∂Ω), p > 1, λ > 0 and 0 < ν ≤ p. Moreover, g, q and f are nonnegative functions verifying suitable hypotheses. The main goal of this work is to analyze the interaction between the functions d, g and the gradient term to get existence and nonexistence results. The singular behavior of g near 0 will provide a new phenomenon that does not appear in the case where the absorption term g(u) q(d(x)) is dropped or substituted by a regular one.
Published Online: 2016-03-10
Published in Print: 2012-02-01
© 2016 by Advanced Nonlinear Studies, Inc.
