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Decaying positive solutions to a system of nonlinear elliptic equations

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Abstract:

In this paper, the second-order nonlinear elliptic system

−Δu = f1(x)uαg1(x)u + h1(x)uP(v),

−Δu = f2(x)vαg2(x)v + h2(x) vP(v),

with α,  < 1 and ≥ 1, is considered in RN, N ≥ 3. 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) ∈ C2, loc(RN) × C2, loc(RN), 0 < < 1, such that both u and v are bounded below and above by constant multiples of |x|2−N for all |x| ≥1.

Document Type: Research Article

Publication date: May 1, 2006

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