Large solutions of coupled sublinear/superlinear elliptic equations |
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Authors: | Jesse Peterson David Smith |
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Institution: | Department of Mathematics and Statistics , Air Force Institute of Technology , Wright-Patterson AFB, OH 45433-7765, USA |
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Abstract: | We show that large positive solutions exist for the semilinear elliptic equation Δu = p(x)u α + q(x)v β on bounded domains in R n , n ≥ 3, for the superlinear case 0 < α ≤ β, β > 1, but not the sublinear case 0 < α ≤ β ≤ 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. |
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Keywords: | large solution semilinear elliptic equation |
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