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Equilibria and stabilities for competing-species reaction-diffusion equations with Dirichlet boundary data. (English) Zbl 0427.35011

35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
92D40 Ecology
Full Text: DOI
[1] Amann, H., On the existence of positive solutions of nonlinear elliptic boundary value problems, Indiana univ. math. J., 21, 125-146, (1971) · Zbl 0209.13002
[2] Bradford, E.; Philip, J.R., Stability of steady distributions of asocial populations dispersing in one dimension, J. theoret. biol., 29, 13-26, (1970)
[3] Casten, R.; Holland, C., Stability properties of solutions to systems of reaction-diffusion equations, SIAM J. appl. math., 33, 353-364, (1977) · Zbl 0372.35044
[4] Chueh, K.N.; Conley, C.C.; Smoller, J.A., Positively invariant regions for systems of nonlinear diffusion equations, Indiana univ. math. J., 26, 373-392, (1977) · Zbl 0368.35040
[5] \scD. Clark, On differential inequalities for systems of diffusion-reaction type, to appear.
[6] Conway, E.; Smoller, J., Diffusion and the predator-prey interaction, SIAM J. appl. math., 33, 673-686, (1977) · Zbl 0368.35021
[7] Courant, R.; Hilbert, D., ()
[8] Hilborn, R., The effect of spatial heterogeneity on the persistence of predator-prey interactions, Theoret. population biol., 8, 346-355, (1975)
[9] Lady┼żenskaja, O.A.; Solonnikov, V.A.; Ural’cera, N.N., Linear and quasilinear equations of parabolic type, ()
[10] Leung, A., Limiting behavior for a prey-predator model with diffusion and crowding effects, J. math. biol., 6, 87-93, (1978) · Zbl 0386.92011
[11] \scA. Leung and D. Clark, Bifurcations and large-time asymptotic behavior for prey-predator reaction-diffusion equations with Dirichlet boundary data, to appear. · Zbl 0427.35014
[12] Levin, S., Spatial patterning and the structure of ecological communities, () · Zbl 0338.92017
[13] Maynard-Smith, J., Models in ecology, (1974), Cambridge Univ. Press Cambridge, England · Zbl 0312.92001
[14] Protter, M.H.; Weinberger, H., Maximum principles in differential equations, (1967), Prentice-Hall Engelwood Cliffs, N.J., · Zbl 0153.13602
[15] Sattinger, D.H., Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana univ. math. J., 21, 979-1000, (1972) · Zbl 0223.35038
[16] Sattinger, D.H., Topics in stability and bifurcation theory, () · Zbl 0466.58016
[17] Tsai, L.Y., Nonlinear boundary value problems for systems of second order elliptic differential equations, Bull. inst. math. acad. sinica, 5, 157-165, (1977) · Zbl 0356.35029
[18] Williams, S.; Chow, P.L., Nonlinear reaction-diffusion models for interacting populations, J. math. anal. appl., 62, 157-169, (1978) · Zbl 0372.35047
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