• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.123-132
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• 1995

Our interest is to study the existence of positive solutions to the following elliptic system involving competing interaction $$ (1) { -\partial(x,u,\upsilon)\Delta u = uf(x,u,v) { - \psi(x,u,\upsilon)\Delta \upsilon = \upsilon g(x,u,\upsilon) { \frac{\partial n}{\partial u} + ku = 0 on \partial\Omega { \frac{\partial n}{\partial\upsilon} + \sigma\upsilon = 0 $$ in a bounded region $\Omega$ in $R^n$ with a smooth boundary, where the diffusion terms $\varphi, \psi$ are strictly positive nondecreasing function, and k, $\sigma$ are positive constants. Also we assume that the growth rates f, g are $C^1$ monotone functions. The variables u, $\upsilon$ may represent the population densities of the interacting species in problems from ecology, microbiology, immunology, etc.