Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

UNIQUENESS OF POSITIVE STEADY STATES FOR WEAK COMPETITION MODELS WITH SELF-CROSS DIFFUSIONS

  • Published : 2004.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we investigate the uniqueness of positive solutions to weak competition models with self-cross diffusion rates under homogeneous Dirichlet boundary conditions. The methods employed are upper-lower solution technique and the variational characterization of eigenvalues.

Keywords

References

  1. Proc. Roy. Soc. Edinburgh Sect. v.A97 Bifurcation of steady state solutions in predator-prey and competition systems J.Blat;K.J.Brown
  2. Houston J. Math. v.13 no.3 On the steady-state problem for the Volterra-Lotka competition model with diffusion R.S.Cantrell;C.Cosner
  3. Houston J. Math. v.15 no.3 On the uniqueness and stability of positive solutions in the Latka-Volterra competition model with diffusion R.S.Cantrell;C.Cosner
  4. SIAM J. Appl. Math. no.6 Stable coexistence states in the Volterra-Lotka competition model with diffusion C.Cosner;A.C.Lazer
  5. Trans. Amer. Math. Soc. v.326 no.2 On the existence and uniqueness of positive solutions for competing species models with diffusion E.Dancer https://doi.org/10.2307/2001785
  6. Bull. Austral. Math. Soc. v.44 no.1 Positive solutions of a class of biological models in a heterogenious environment A.Ghoreishi;R.Logan https://doi.org/10.1017/S0004972700029488
  7. Appl. Anal. v.40 no.4 On positive solutions of general nonlinear elliptic symbiotic interacting systems L.Li;A.Ghoreishi https://doi.org/10.1080/00036819108840010
  8. J. Differential Equations v.131 no.1 Diffusion, self-diffusion and cross-diffusion Y.Lou;W.M.Ni https://doi.org/10.1006/jdeq.1996.0157
  9. Appl. Anal. v.26 no.2 On existence and uniqueness of positive steady-state in the Volterra-Latka ecological models with diffusion P.Korman;A.Leung https://doi.org/10.1080/00036818708839706
  10. P. J. McKenna and W. Walter, On the Dirichlet problem for elliptic systems, Appl. Anal. 21 (1986), no. 3, 207-224. https://doi.org/10.1080/00036818608839592
  11. K. Ryu and I. Ahn, Positive steady-states for two interacting species models with linear self-cross diffusions, Discrete Contino Dyn. Syst. 9 (2003), no. 4, 1049-1061. https://doi.org/10.3934/dcds.2003.9.1049