Instability of stationary solutions for a Lotka-Volterra competition model with diffusion

Journal of Mathematical Analysis and Applications

Volumn 208, Issue 1, 1997, Pages 158-170

  Kan on, Yukio ^a  

^a EHIME UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; PROBLEM SOLVING; STABILITY; THEOREM PROVING;

LOTKA-VOLTERRA COMPETITION MODEL; STATIONARY SOLUTIONS;

MATHEMATICAL MODELS;

EID: 0031106934     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5309     Document Type: Article

References (10)

1. Alexander J., Gardner R., Jones C. A topological invariant arising in the stability analysis of travelling waves. J. Reine Angew. Math. 410:1990;167-212.
2. Ali S. W., Cosner C. On the uniqueness of the positive steady state for Lotka-Volterra model with diffusion. J. Math. Anal. Appl. 168:1992;329-341.
3. Bates P. W., Jones C. K. R. T. Invariant manifolds for semilinear partial differential equations. Kirchgraber U. Dynamics Reported. 1989;1-38 Wiley, Chichester.
4. Coddington E. A., Levinson N. Theory of Ordinary Differential Equations. 1955;McGraw-Hill, New York.
5. Coppel W. A. Dichotomies in Stability Theory. 1978;Springer-Verlag, Berlin.
6. Cosner C., Lazer A. C. Stable coexistence states in the Volterra-Lotka competition model with diffusion. SIAM J. Appl. Math. 44:1984;1112-1132.
7. Derndinger R. Über das Spectrum positiver Generatoren. Math. Z. 172:1980;281-293.
8. Kan-on Y. Existence of standing waves for competition-diffusion equations. Japan J. Indust. Appl. Math. 13:1996;117-133.
9. Kan-on Y., Yanagida E. Existence of non-constant stable equilibria in competition-diffusion equations. Hiroshima Math. J. 23:1993;193-221.
10. Mimura M., Fife P. C. A 3-component system of competition and diffusion. Hiroshima Math. J. 16:1986;189-207.