Publication Cover
Applicable Analysis
An International Journal
Volume 44, 1992 - Issue 3-4
56
Views
15
CrossRef citations to date
0
Altmetric
Original Articles

Dynamics of the lotka-volterra systems with diffusion

Pages 191-207 | Received 23 Oct 1990, Published online: 02 May 2007

References

  • Amann , H. 1978 . Invariant sets and existence theorems for semi linear parabolic and elliptic systems . J. Math. Anal. Applic , 65 : 432 – 467 .
  • Babin , A.V. and Vishik , M.I. 1989 . Attractors of Evolution Equations , Moscow : Nauka . Russian
  • Dancer , E.N. 1984 . On positive solutions of some pairs of differential equations . Trans. Amer. Math. Soc , 284 : 729 – 743 .
  • E.N. Dancer, On the existence and uniqueness of positive solutions for competing species modelswith diffusion, Preprint
  • B. Fiedler and P. Polačik, Complicated dynamics of scalar reaction diffusion equations with a nonlocal term, Preprint
  • Friedman , A. 1964 . Partial Differential Equations of Parabolic Type , N.J : Prentice-Hall .
  • Korman , P. and Leung , A. 1986 . A general monotone scheme for elliptic systems with applications to ecological models . Proc. Royal Soc. Edinburgh , 102 ( A ) : 315 – 325 .
  • Korman , P. and Leung , A. 1987 . On the existence and uniqueness of positive steady states in the Volterra-Lotka ecological models with diffusion . Applicable Analysis , 26 ( A ) : 145 – 160 .
  • Levine , H.A. 1973 . Some nonexistence and instability theorems for solutions of formally parabolic equation . Arch. Rational Mech. Anal , 51 ( A ) : 371 – 386 .
  • Matano , H. 1979 . Asymptotic behavior and stability of solutions of semilinear diffusion equations . Publ. RIMS, Kyoto Univ , 15 ( A ) : 401 – 454 .
  • Mc Kenna , P.J. and Walter , W. 1986 . On the Dirichlet problem for elliptic systems . Applicable Analysis , 21 ( A ) : 207 – 224 .
  • Sattinger , D.H. 1972 . Monotone methods in nonlinear elliptic and parabolic boundary value problems . Indiana Univ. Math. J , 21 ( A ) : 979 – 1000 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.