Title of article :
Non-constant positive steady states of a prey–predator
system with cross-diffusions
Author/Authors :
Xianzhong Zeng، نويسنده , , b، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2007
Abstract :
In this paper, we study a strongly coupled elliptic system arising from a Lotka–Volterra prey–predator
system, where cross-diffusions are included in such a way that the prey runs away from the predator and the
predator moves away from a large group of preys. We establish the existence and non-existence of its nonconstant
positive solutions. Our results show that if m1b < a <2m1b/(1−m1m2) when 0m1b when m1m2 1, 0 < d1 < (m1 ˜v − ˜u)/μ1, d2 > 0, d3 0 and d4 > 1/(m1 ˜v − ˜u), then there
exists (d1, d2, d3, d4) such that the stationary problem admits non-constant positive solutions. Otherwise,
the stationary problem has no non-constant positive solution. In particular, the results indicate that its nonconstant
positive solutions are mainly created by the cross-diffusion d4.
© 2006 Elsevier Inc. All rights reserved
Keywords :
Non-constant positive steady-states , Degree theory , Prey–predator system , cross-diffusion
Journal title :
Journal of Mathematical Analysis and Applications
Journal title :
Journal of Mathematical Analysis and Applications