Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
844623 | Nonlinear Analysis: Theory, Methods & Applications | 2007 | 7 Pages |
Abstract
We consider the system −Δu=λf(v);x∈Ω−Δv=μg(u);x∈Ωu=0=v;x∈∂Ω where ΩΩ is a ball in RNRN, N≥1N≥1, and ∂Ω∂Ω is its boundary, λ,μλ,μ are positive parameters, and f,gf,g are smooth functions that are negative at the origin and f(x)∼xpf(x)∼xp and g(x)∼xqg(x)∼xq for large xx for some p,q≥0p,q≥0 with pq<1pq<1. We establish the uniqueness of positive solutions when the parameters λλ and μμ are large.
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Authors
D.D. Hai, R. Shivaji,