Existence of positive solutions for a class of singular and quasilinear elliptic problems with critical exponential growth

Abstract

In this paper we use Galerkin method to investigate the existence of positive solution for a class of singular and quasilinear elliptic problems given byand its version for systems given bywhere Ω ⊂ R N is bounded smooth domain with N ≥ 3 and for i = 0, 1, 2 we have 2 ≤ p i < N , 0 < β i ≤ 1, λ i > 0 and f i are continuous functions. The hypotheses on the C 1 -functions a i : R + → R + allow to consider a large class of quasilinear operators.