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The uniqueness of positive solution in competition model

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Abstract

In this paper, we investigate the uniqueness of positive solutionsto weak competition models with self-cross diffusion rates underhomogeneous Dirichlet boundary conditions. The methods employedare upper-lower solution technique and the variationalcharacterization of eigenvalues.

참고문헌 (12)

  1. Blat, "Bifurcation of steady state solutions in predator-prey andcompetition systems", 97, pp.21~ (1984)
  2. S. Cantrell, "On the steady-state problem for the Volterra-Lotka competitionmodel with diffusion", 13(3), pp.337~ (1987)
  3. On the uniqueness, "Houston J.Math. 15(1989", no. 3
  4. Cosner, "Stable coexistence statesin the Volterra-Lotka competition model with diffusion", (6), pp.1112~ (1984)
  5. Dancer, "On the existence and uniqueness of positivesolutions for competing species models with diffusion", 326(2), pp.829~ (1991)
  6. Ghoreishi, "Positive solutions of a class of biological models in aheterogenious environment", 44(1), pp.79~ (1991)
  7. Li, "On positive solutions of generalnonlinear elliptic symbiotic interacting systems", 40(4), pp.281~ (1991)
  8. Y. Lou, "Diffusion, self-diffusion andcross-diffusion", (1), pp.79~131 (1996)
  9. Korman, "On existence and uniquenessof positive steady-state in the Volterra-Lotka ecological modelswith diffusion", 26(2), pp.145~ (1987)
  10. "On the Dirichletproblem for elliptic systems", 21(3), pp.207~ (1986)
  11. "Positive steady--states for twointeracting species models with linear self--cross diffusions", 9(4), pp.1049~1061 (2003)
  12. "Positive steady--states for twointeracting species models with linear self--cross diffusions", 9(4), pp.1049~1061 (2003)

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