In this paper, we are interested in the following singular problem: [Formula: see text] where 0 < p ∈ L∞, λ > 0, 0 < δ < 3, Ω a smooth bounded domain. We show on suitable conditions on h there exist two solutions in [Formula: see text]. Investigating the radial case, we are able to prove that the condition at infinity for h is optimal for getting the existence of the second solution.
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Adimurthi et al. (2006) studied this question.
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