Elliptic Systems Involving Competing Interactions With Nonlinear Diffusions II
Commun. Korean Math. Soc. 1997 Vol. 12, No. 4, 869-880
In Kyung Ahn
Korea University
Abstract : In this paper, we give sufficient conditions of certain elliptic systems involving competing interactions with nonlinear diffusion rates. The existence of positive solution depends on the sign of the first eigenvalue of operators of Schr{\"o}dinger type. More precisely, if the sign of such operators are either both positive or both negative, then system has a positive solution. The main tool employed is the fixed point index of compact operator on positive cones.
Keywords : Competing interaction, Nonlinear diffusions, Fixed point index
MSC numbers : 35J60
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