MR2538281 Kazuhiro OEDA Kazuhiro OEDA Stationary Patterns for a Lotka-Volterra Cooperative Model with a Density-Dependent Diffusion Term Funkcialaj Ekvacioj. Serio Internacia 52 2009 93--112 http://fe.math.kobe-u.ac.jp/FE/FullPapers/52-1/52_93.pdf http://www.ams.org/mathscinet-getitem?mr=MR2538281 This paper is concerned with positive stationary solutions for a Lotka-Volterra cooperative model with a density-dependent diffusion term of a fractional type. The existence of stationary patterns is proven by the presence of density-dependent diffusion. Our proof is based on the Leray-Schauder degree theory and some a priori estimates. We also derive a certain limiting system which positive stationary solutions satisfy. Cooperative model, Density-dependent diffusion, Stationary patterns, Leray-Schauder degree theory, Limiting system. Primary 35J65; Secondary 35B40, 35K57, 92D25. 52-93 2009 Stationary Patterns for a Lotka-Volterra Cooperative Model with a Density-Dependent Diffusion Term Kazuhiro OEDA Kazuhiro OEDA
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