Abstract
Let be a smooth bounded domain in R n ; n 2: This paper deals with the existence and the asymptotic behavior of positive solutions of the following problems u = a(x)u ; > 1 and u = a(x)e u ; with the boundary conditionuj@ = +1: The weight functiona(x) is positive inC loc () ; 0 < < 1, and satises an appropriate assumption related to Karamata regular variation theory. Our arguments are based on the sub-supersolution method.
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