| Abstract: |
| We consider a m-component competition-diffusion system, and prove the following results : If the carrying capacity of the population of density u_m tends to infinity, then all populations except for the mth-population disappear while the mth population not only remains but becomes infinitely large; if the carrying capacity of the population of density u_m is large enough, then all populations except for the mth-population disappear while the mth population not only remains but become infinitely large as time tends to infinity. If the carrying capacity of the population of density u_m tends to zero, then all populations probably remain except for the mth-population which vanishes. If the carrying capacity of the population of density u_m is small enough, and if all the other populations diffuse at an equal rate, then all populations probably remain except for the mth-population which disappears in large time. |
|