Existence of Positive Solutions for some Dirichlet Problems with an Asymptotically Homogenous Operator
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Existence of positive radially symmetric solutions to a Dirichlet prob- lem of the form −div(A(|Du|)Du) = f(u) in Ω u = 0 on ∂Ω is studied by using blow-up techniques. It is proven here that by choosing the functions sA(s) and f(s) among a certain class called asymptotically homogeneous, the blow-up method still provides the a-priori bounds for positive solutions. Existence is proved then by using degree theory.