Coexistence states of a three-species cooperating model with diffusion

References

• Dancer , EN and Du , YH . 1995 . Positive solutions for a three-species competition system with diffusion-I: General existence results . Nonlinear Anal. , 24 : 337 – 357 .
   Google Scholar
• Dancer , EN and Du , YH . 1995 . Positive solutions for a three-species competition system with diffusion-II: The case of equal birth rates . Nonlinear Anal. , 24 : 359 – 373 .
   Google Scholar
• Lakos , N . 1990 . Existence of steady state solutions for a one-predator-two-prey system . SIAM J. Math. Anal. , 21 : 647 – 659 .
   Google Scholar
• Hsiao , L and Mottoni , PD . 1987 . Persistence in reaction-diffusion systems: Interaction of two predators and one prey . Nonlinear Anal. , 11 : 877 – 891 .
   Google Scholar
• Hei , LJ and Wu , JH . 2005 . Existence and stability of positive solutions for an elliptic cooperative systems . Acta Math. Sin. , 21 : 1113 – 1120 .
   Google Scholar
• Kim , KI and Lin , ZG . 2004 . Blowup in a three-species cooperating model . Appl. Math. Lett. , 17 : 89 – 94 .
   Google Scholar
• Kim , KI and Lin , ZG . 2004 . Blowup estimates for a parabolic system in a three-species cooperating model . J. Math. Anal. Appl. , 293 : 663 – 676 .
   Google Scholar
• López-Gómez , J . 1992 . Positive periodic solutions of Lotka–Volterra reaction-diffusion systems . Differ. Integral Equ. , 5 : 55 – 72 .
   Google Scholar
• Wang , LZ and Li , KT . 2003 . On positive solutions of the Lotka–Volterra cooperating models with diffusion . Nonlinear Anal. , 53 : 1115 – 1125 .
   Google Scholar
• Wu , JH and Wei , GS . 2002 . Coexistence states for cooperative model with diffusion . Comput. Math. Appl. , 43 : 1277 – 1290 .
   Google Scholar
• Lou , Y . 1996 . Necessary and sufficient condition for the existence of positive solutions of certain cooperative systems . Nonlinear Anal. , 26 : 1079 – 1095 .
   Google Scholar
• Delgado , M , López-Gómez , J and Suárez , A . 2000 . On the symbiotic Lotka–Volterra model with diffusion and transport effects . J. Differ. Equ. , 160 : 175 – 262 .
   Google Scholar
• Pao , CV . 2000 . Periodic solutions of systems of parabolic equations in unbounded domains . Nonlinear Anal. , 40 : 523 – 535 .
   Google Scholar
• Hess , P . 1991 . Periodic-parabolic Boundary Value Problems and Positivity, Pitman Research Notes in Mathematical Series , Vol. 247 , New York : Longman Scientific and Technical .
   Google Scholar
• Brown , KJ and Hess , P . 1991 . Positive periodic solutions of predator-prey reaction-diffusion systems . Nonlinear Anal. , 16 : 1147 – 1158 .
   Google Scholar
• Fu , SM and Ma , RY . 1997 . Existence of a global coexistence state for periodic competition diffusion systems . Nonlinear Anal. , 28 : 1265 – 1271 .
   Google Scholar
• Leung , A and Ortega , L . 1998 . Existence and monotone scheme for time-periodic nonquasimonotone reaction-diffusion systems: Application to autocatalytic chemistry . J. Math. Anal. Appl. , 221 : 712 – 733 .
   Google Scholar
• Tineo , A . 1992 . Existence of global coexistence state for periodic competition diffusion systems . Nonlinear Anal. , 19 : 335 – 344 .
   Google Scholar
• Jia , YF and Wu , JH . 2007 . Asymptotic behaviour of solutions of a periodic reaction-diffusion system of a three-species of competition model . Appl. Math. Comput. , 189 : 1683 – 1693 .
   Google Scholar
• Cosner , RC and Lazer , AC . 1984 . Stable coexistence state in the Volterra-Lotka competition model with diffusion . SIAM J. Appl. Math. , 44 : 1112 – 1132 .
   Google Scholar
• Pao , CV . 1999 . Periodic solutions of parabolic systems with nonlinear boundary conditions . J. Math. Anal. Appl. , 234 : 695 – 716 .
   Google Scholar
• Schaefer , HH . 1966 . Topological Vector Spaces , New York : Macmillan .
   Google Scholar
• Keener , J . 1987 . Principles of Applied Mathematics , Reading, MA : Addison-Wesley .
   Google Scholar
• Zhong , CK , Fan , XL and Chen , WY . 2004 . Introduction to Nolinear Functional Analysis , Lanzhou : Lanzhou University Press .
   Google Scholar
• Li , LG and Logan , R . 1991 . Positive solutions to general elliptic competition models . Differ. Integral Equ. , 4 : 817 – 834 .
   Google Scholar