Permanence under strong aggressions is possible
Cano-Casanova, Santiago ; López-Gómez, Julián
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003), p. 999-1041 / Harvested from Numdam
@article{AIHPC_2003__20_6_999_0,
     author = {Cano-Casanova, Santiago and L\'opez-G\'omez, Juli\'an},
     title = {Permanence under strong aggressions is possible},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {20},
     year = {2003},
     pages = {999-1041},
     doi = {10.1016/S0294-1449(03)00022-2},
     mrnumber = {2008687},
     zbl = {1086.35054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2003__20_6_999_0}
}
Cano-Casanova, Santiago; López-Gómez, Julián. Permanence under strong aggressions is possible. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) pp. 999-1041. doi : 10.1016/S0294-1449(03)00022-2. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_6_999_0/

[1] Amann H, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math. 45 (1983) 225-254. | MR 719122 | Zbl 0535.35017

[2] Amann H, Linear and Quasilinear Parabolic Problems, Monographs Math., 89, Birkhäuser, Basel, 1995. | MR 1345385 | Zbl 0819.35001

[3] Amann H, López-Gómez J, A priori bounds and multiple solutions for superlinear indefinite elliptic problems, J. Differential Equations 146 (1998) 336-374. | MR 1631287 | Zbl 0909.35044

[4] Begon M, Harper J.L, Townsend C.R, Ecology, Individual, Populations and Communities, Blackwell Scientific Publications, Cambridge, MA, 1990.

[5] Cano-Casanova S, Existence and structure of the set of positive solutions of a general class of sublinear elliptic non-classical mixed boundary value problems, Nonlinear Anal. 49 (2002) 361-430. | MR 1886119 | Zbl 01730246

[6] Cano-Casanova S, López-Gómez J, Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems, J. Differential Equations 178 (2002) 123-211. | MR 1878528 | Zbl 1086.35073

[7] S. Cano-Casanova, J. López-Gómez, Varying domains in a general class of sublinear elliptic problems, submited. | Zbl 1109.35352

[8] Cantrell R.S, Cosner C, On the effects of spatial heterogeneity on the persistence of interacting species, J. Math. Biol. 37 (1998) 103-145. | MR 1649516 | Zbl 0948.92021

[9] Cantrell R.S, Cosner C, Hutson V, Permanence in some diffusive Lotka-Volterra models for three interacting species, Dynamic Systems Appl. 2 (1993) 505-530. | MR 1249389 | Zbl 0795.92030

[10] Dancer E.N, On the existence and uniqueness of positive solutions for competing species models with diffusion, Trans. Amer. Math. Soc. 326 (1991) 829-859. | MR 1028757 | Zbl 0769.35016

[11] Dancer E.N, Positivity of maps and applications, in: Matzeu M, Vignoli A (Eds.), Topological Nonlinear Analysis, Degree, Singularities and Variations, Progr. Nonlinear Differential Equations Appl., 15, Birkhäuser, Basel, 1995, pp. 303-340. | MR 1322326 | Zbl 0845.47043

[12] Hess P, Periodic-Parabolic Boundary Value Problems and Positivity, Longman, Harlow, 1991. | MR 1100011 | Zbl 0731.35050

[13] Hess P, Lazer A.C, On an abstract competition model and applications, Nonlinear Anal. 16 (1991) 917-940. | MR 1106994 | Zbl 0743.35033

[14] Hirsch M, Stability and convergence in strongly monotone dynamical systems, J. Reine Angew. Math. 383 (1988) 1-58. | MR 921986 | Zbl 0624.58017

[15] Hsu S.B, Smith H.L, Waltman P, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Trans. Amer. Math. Soc. 348 (1996) 4083-4094. | MR 1373638 | Zbl 0860.47033

[16] López-Gómez J, Permanence under strong competition, World Sci. Ser. Appl. Anal., 4, Word Sci. Publishing, River Edge, NJ, 1995, 473-488. | MR 1372977 | Zbl 0854.35055

[17] López-Gómez J, The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems, J. Differential Equations 127 (1996) 263-294. | MR 1387266 | Zbl 0853.35078

[18] López-Gómez J, Molina-Meyer M, The maximum principle for cooperative weakly coupled elliptic systems and some applications, Differential Integral Equations 7 (1994) 383-398. | MR 1255895 | Zbl 0827.35019

[19] López-Gómez J, Sabina J.C, Coexistence states and global attractivity for some convective diffusive competition models, Trans. Amer. Math. Soc. 347 (1995) 3797-3833. | MR 1311910 | Zbl 0848.35012

[20] Murray J.D, Mathematical Biology, Biomathematics Texts, 19, Springer, Berlin, 1989. | MR 1007836 | Zbl 0682.92001

[21] Neças J, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. | MR 227584

[22] Okubo A, Diffusion and Ecological Problems: Mathematical Models, Springer, Berlin, 1980. | MR 572962 | Zbl 0422.92025

[23] Schaefer H.H, Topological Vector Spaces, Springer, New York, 1971. | MR 342978 | Zbl 0217.16002

[24] Smith H.L, Thieme H.R, Stable coexistence and bio-stability for competitive systems of ordered banach spaces, J. Differential Equations 176 (2001) 195-222. | MR 1861187 | Zbl 1064.47075

[25] Stein E.M, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970. | MR 290095 | Zbl 0207.13501

[26] Takác P, Discrete monotone dynamics and time periodic competition between two species, Differential Integral Equations 10 (1997) 547-576. | MR 1744861 | Zbl 0890.35012

[27] Wilson E.O, Sociobiology, Harvard University Press, Cambridge, MA, 1980.