Large solutions of coupled sublinear/superlinear elliptic equations
We show that large positive solutions exist for the semilinear elliptic equation Δu = p(x)uα + q(x)v on bounded domains in Rn, n ≥ 3, for the superlinear case 0 < α ≤ , > 1, but not the sublinear case 0 < α ≤ ≤ 1. We also show that entire large positive solutions exist for both the superlinear and sublinear cases provided the nonnegative continuous functions p and q satisfy certain decay conditions at infinity. Existence and nonexistence of entire bounded solutions are established as well.
Keywords: large solution; semilinear elliptic equation
Document Type: Research Article
Affiliations: Department of Mathematics and Statistics, Air Force Institute of Technology, OH 45433-7765, USA
Publication date: 01 June 2010
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