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Positive solutions of certain elliptic systems with density-dependent diffusions

Published online by Cambridge University Press:  14 November 2011

Inkyung Ahn  and
Lige Li
Inkyung Ahn
Affiliation:
Department of Mathematics, Kansas State University, Manhattan, KS 66506, U.S.A
Lige Li
Affiliation:
Department of Mathematics, Kansas State University, Manhattan, KS 66506, U.S.A
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Extract

Results are obtained on the existence of positive solutions to the following elliptic system:

in a bounded region Ω in Rn 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 5 , 1995 , pp. 1031 - 1050
Copyright
Copyright © Royal Society of Edinburgh 1995

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