Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591207 | Journal of Functional Analysis | 2010 | 29 Pages |
Abstract
We classify all the possible asymptotic behavior at the origin for positive solutions of quasilinear elliptic equations of the form div(|∇u|p−2∇u)=b(x)h(u) in Ω∖{0}, where 1
0) and the weight function b(x) behaves near the origin as a function b0(|x|) varying regularly at zero with index θ greater than −p. This condition includes b(x)=θ|x| and some of its perturbations, for instance, b(x)=θ|x|m(−log|x|) for any m∈R. Our approach makes use of the theory of regular variation and a new perturbation method for constructing sub- and super-solutions.
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