Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지

ELLIPTIC SYSTEMS INVOLVING COMPETING INTERACTIONS WITH NONLINEAR DIFFUSIONS II

  • Published : 1997.10.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we give sufficient conditions of certain elliptic systems involving competing iteractions with nonlinear diffusion rates. The existence of positive solution depends on the sign of the first eigenvalue of operators of Schr$\ddot{o}$dinger type. More precisely, if the sign of such operators are either both positive or both negative, then system has a positive solution. The main tool employed is the fixed point index of compact operator on positive cones.

Keywords

References

  1. J. Korean Math. Soc. v.31 Positive solutions for predator-prey equations with nonlinear diffusion rates I. Ahn
  2. Bull. Korean Math. Soc. v.32 Elliptic systems incvolving competing interactions with nonlinear diffusions I. Ahn
  3. SIAM Rev. v.18 Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces H. Amann
  4. Proc. Roy. Soc. Edinburgh v.(A)97 Bifurcation of steady-states solution in predator-prey and competition systems J. Blat;K. Brown
  5. J. Math. Anal. Appl. v.91 On the indices of fixed points of mappings in cones and applications E. N. Dancer
  6. J. Diff. Equ. v.60 On positive solutions of some pairs of differential equations II E. N. Dancer
  7. Spectral theory and differential operators D. E. Edmunds;W. P. Evans
  8. J. Math. Anal. Appl. v.123 Existence of steady-state solutions to predator-prey equations in a heterogeneous environment C. Keller;R. Lui
  9. Amer. Math. Soc. v.305 Coexistence theorems of steady-state for predator-prey interacting systems L. Li
  10. J. of Diff. & Integ Eqs. v.4 Positive solutions to general elliptic competition models L. Li;R. Logan
  11. J. Math. Anal. Appl. v.87 C. V. Pao On nonlinear reaction-diffusion systems
  12. Shock waves and reaction-diffusion dquations J. Smoller