Positive solutions for nonhomogeneous elliptic equations involving critical Sobolev exponent

Abstract

In this paper, we study the existence and multiplicity of positive solutions for the Dirichlet problem − Δ u = λ f ( z ) | u | q − 2 u + g ( z ) | u | 2 ∗ − 2 u in Ω , where λ > 0 , 1 ≤ q < 2 , 2 ∗ = 2 N / ( N − 2 ) , 0 ∈ Ω ⊂ R N ( N ≥ 3 ) is a bounded domain with smooth boundary ∂ Ω , and f , g are nonnegative continuous functions on Ω ¯ .