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Entire large solutions for semilinear elliptic equations
We analyze the semilinear elliptic equation , in
, with a particular emphasis put on the qualitative
study of entire large solutions, that is, solutions such that
. Assuming that satisfies the
Keller-Osserman growth assumption and that decays at infinity in a
suitable sense, we prove the existence of entire large solutions. We then
discuss the more delicate questions of asymptotic behavior at infinity,
uniqueness and symmetry of solutions.Comment: Journal of Differential Equations 2012, 28 page
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