Entire positive solution to the system of nonlinear elliptic equations

Lingyun Qiu, Miaoxin Yao

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The second-order nonlinear elliptic system - Δu = f1 (x)uα + g1(x)u + h1(x)uγP(v), - Δv = f2 (x)vα + g2(x)v + h2(x)vγP(u) with 0 < α, β, γ < 1, is considered in Rdbl;N. Under suitable hypotheses on functions fi, gi, hi (i = 1,2), and P, it is shown that this system possesses an entire positive solution (u,v) ∈ ℂloc2,θ (ℝN) × ℂloc2,θ (ℝN) (0 < θ < 1) such that both u and v are bounded below and above by positive constant multiples of x 2-N for all x ≥ 1.

Original languageEnglish (US)
Article number32492
JournalBoundary Value Problems
StatePublished - 2006

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Copyright 2006 Elsevier B.V., All rights reserved.

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