Asymptotic behavior of solutions of semilinear elliptic equations near an isolated singularity |
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| Authors: | Florica Corina Cîrstea Yihong Du |
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| Institution: | aDepartment of Mathematics, Mathematical Sciences Institute, The Australian National University, Canberra, ACT 0200, Australia;bSchool of Mathematics, Statistics and Computer Science, University of New England, Armidale, NSW 2351, Australia;cDepartment of Mathematics, Qufu Normal University, PR China |
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| Abstract: | We consider the semilinear elliptic equation Δu=h(u) in Ω {0}, where Ω is an open subset of  (N 2) containing the origin and h is locally Lipschitz continuous on 0,∞), positive in (0,∞). We give a complete classification of isolated singularities of positive solutions when h varies regularly at infinity of index q (1,CN) (that is, limu→∞h(λu)/h(u)=λq, for every λ>0), where CN denotes either N/(N−2) if N3 or ∞ if N=2. Our result extends a well-known theorem of Véron for the case h(u)=uq. |
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| Keywords: | Isolated singularity Elliptic equation Regularly varying functions |
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