Positive solutions of certain elliptic systems with density-dependent diffusions

Results are obtained on the existence of positive solutions to the following elliptic system: in a bounded region Ω in R n with a smooth boundary, where the diffusion terms φ ψ are non-negative functions and the system could be degenerate, β γ are strictly increasing functions, k,σ ≧ 0 are constants. We assume also that the growth rates f, g satisfy certain monotonicities. Applications to biological interactions with density-dependent diffusions are given.

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