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Volumn 283, Issue 1, 2003, Pages 46-65

Coexistence theorem of steady states for nonlinear self-cross diffusion systems with competitive dynamics

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EID: 0043133552     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00162-8     Document Type: Article
Times cited : (57)

References (32)
  • 1
    • 0017014016 scopus 로고
    • Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces
    • H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976) 620-709.
    • (1976) SIAM Rev. , vol.18 , pp. 620-709
    • Amann, H.1
  • 2
    • 0011403472 scopus 로고
    • A density-dependent diffusion system with stable discontinuous stationary solutions
    • D.G. Aronson, A. Tesei, H. Weinberger, A density-dependent diffusion system with stable discontinuous stationary solutions, Ann. Mat. Pura Appl. (4) 152 (1988) 259-280.
    • (1988) Ann. Mat. Pura Appl. , vol.152 , Issue.4 , pp. 259-280
    • Aronson, D.G.1    Tesei, A.2    Weinberger, H.3
  • 3
    • 80052954107 scopus 로고
    • Bifurcation of steady-state solutions in predator-prey and competition systems
    • J. Blat, K.J. Brown, Bifurcation of steady-state solutions in predator-prey and competition systems, Proc. Roy. Soc. Edinburgh Sect. A 97 (1984) 21-34.
    • (1984) Proc. Roy. Soc. Edinburgh Sect. A , vol.97 , pp. 21-34
    • Blat, J.1    Brown, K.J.2
  • 4
    • 85031139226 scopus 로고    scopus 로고
    • Some remarks about the existence of positive solutions for elliptic systems
    • (Tampa, FL, 1992), de Gruyter, Berlin
    • A. Cañada, J.L. Gámez, Some remarks about the existence of positive solutions for elliptic systems, in: World Congress of Nonlinear Analysts '92, Vols. I-IV (Tampa, FL, 1992), de Gruyter, Berlin, 1996, pp. 167-174.
    • (1996) World Congress of Nonlinear Analysts '92 , vol.1-4 , pp. 167-174
    • Cañada, A.1    Gámez, J.L.2
  • 5
    • 0000213563 scopus 로고
    • Permanence in some diffusive Lotka-Volterra models for three interacting species
    • R.S. Cantrell, C. Cosner, V. Hutson, Permanence in some diffusive Lotka-Volterra models for three interacting species, Dynam. Systems Appl. 2 (1993) 505-530.
    • (1993) Dynam. Systems Appl. , vol.2 , pp. 505-530
    • Cantrell, R.S.1    Cosner, C.2    Hutson, V.3
  • 6
    • 0000907310 scopus 로고
    • On the indices of fixed points of mappings in cones and applications
    • E.N. Dancer, On the indices of fixed points of mappings in cones and applications, J. Math. Anal. Appl. 91 (1983) 131-151.
    • (1983) J. Math. Anal. Appl. , vol.91 , pp. 131-151
    • Dancer, E.N.1
  • 7
    • 84966251421 scopus 로고
    • On the existence and uniqueness of positive solutions for competing species models with diffusion
    • E.N. Dancer, On the existence and uniqueness of positive solutions for competing species models with diffusion, Trans. Amer. Math. Soc. 326 (1991) 829-859.
    • (1991) Trans. Amer. Math. Soc. , vol.326 , pp. 829-859
    • Dancer, E.N.1
  • 8
    • 0002256917 scopus 로고
    • Positive solutions of semilinear elliptic problems
    • (Sao Paulo, 1981), Differential equations., Springer, Berlin
    • D.G. De Figueiredo, Positive solutions of semilinear elliptic problems, in: Differential equations (Sao Paulo, 1981), in: Lecture Notes in Math., Vol. 957, Springer, Berlin, 1982, pp. 34-87.
    • (1982) Lecture Notes in Math , vol.957 , pp. 34-87
    • DeFigueiredo, D.G.1
  • 9
    • 0000329021 scopus 로고
    • An initial-boundary-value problem for a certain density-dependent diffusion system
    • P. Deuring, An initial-boundary-value problem for a certain density-dependent diffusion system, Math. Z. 194 (1987) 375-396.
    • (1987) Math. Z. , vol.194 , pp. 375-396
    • Deuring, P.1
  • 11
    • 0003228130 scopus 로고    scopus 로고
    • Partial Differential Equations
    • American Mathematical Society, Providence
    • L.C. Evans, Partial Differential Equations, in: Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, Providence, 1998.
    • (1998) Graduate Studies in Mathematics , vol.19
    • Evans, L.C.1
  • 12
    • 84971744487 scopus 로고
    • Positive solutions of a class of biological models in a heterogeneous environment
    • A. Ghoreishi, R. Logan, Positive solutions of a class of biological models in a heterogeneous environment, Bull. Austral. Math. Soc. 44 (1991) 79-94.
    • (1991) Bull. Austral. Math. Soc. , vol.44 , pp. 79-94
    • Ghoreishi, A.1    Logan, R.2
  • 13
    • 0002126429 scopus 로고
    • Some mathematical models for population dynamics that lead to segregation
    • M.E. Gurtin, Some mathematical models for population dynamics that lead to segregation, Quart. Appl. Math. 32 (1974/75) 1-9.
    • (1974) Quart. Appl. Math. , vol.32 , pp. 1-9
    • Gurtin, M.E.1
  • 14
    • 0000297309 scopus 로고
    • Smooth solutions to a quasilinear system of diffusion equations for a certain population model
    • J.U. Kim, Smooth solutions to a quasilinear system of diffusion equations for a certain population model, Nonlinear Anal. 8 (1984) 1121-1144.
    • (1984) Nonlinear Anal. , vol.8 , pp. 1121-1144
    • Kim, J.U.1
  • 15
    • 0025495109 scopus 로고
    • Existence of positive solutions for elliptic systems - Degenerate and nondegenerate ecological models
    • A. Leung, G. Fan, Existence of positive solutions for elliptic systems - degenerate and nondegenerate ecological models, J. Math. Anal. Appl. 151 (1990) 512-531.
    • (1990) J. Math. Anal. Appl. , vol.151 , pp. 512-531
    • Leung, A.1    Fan, G.2
  • 16
    • 84966242093 scopus 로고
    • Coexistence theorems of steady states for predator-prey interacting systems
    • L. Li, Coexistence theorems of steady states for predator-prey interacting systems, Trans. Amer. Math. Soc. 305 (1988) 143-166.
    • (1988) Trans. Amer. Math. Soc. , vol.305 , pp. 143-166
    • Li, L.1
  • 17
    • 84963177047 scopus 로고
    • On positive solutions of general nonlinear elliptic symbiotic interacting systems
    • L. Li, A. Ghoreishi, On positive solutions of general nonlinear elliptic symbiotic interacting systems, Appl. Anal. 40 (1991) 281-295.
    • (1991) Appl. Anal. , vol.40 , pp. 281-295
    • Li, L.1    Ghoreishi, A.2
  • 18
    • 84972542454 scopus 로고
    • Positive solutions to general elliptic competition models
    • L. Li, R. Logan, Positive solutions to general elliptic competition models, Differential Integral Equations 4 (1991) 817-834.
    • (1991) Differential Integral Equations , vol.4 , pp. 817-834
    • Li, L.1    Logan, R.2
  • 19
    • 0030579038 scopus 로고    scopus 로고
    • Diffusion, self-diffusion and cross-diffusion
    • Y. Lou, W.M. Ni, Diffusion, self-diffusion and cross-diffusion, J. Differential Equations 131 (1996) 79-131.
    • (1996) J. Differential Equations , vol.131 , pp. 79-131
    • Lou, Y.1    Ni, W.M.2
  • 20
    • 0010995811 scopus 로고
    • Positive solutions of an elliptic system arising from a model in evolutionary ecology
    • R. Lui, Positive solutions of an elliptic system arising from a model in evolutionary ecology, J. Math. Biol. 29 (1991) 239-250.
    • (1991) J. Math. Biol. , vol.29 , pp. 239-250
    • Lui, R.1
  • 21
    • 84972502084 scopus 로고
    • Stationary pattern of some density-dependent diffusion system with competitive dynamics
    • M. Mimura, Stationary pattern of some density-dependent diffusion system with competitive dynamics, Hiroshima Math. J. 11 ( 1981) 621-635.
    • (1981) Hiroshima Math. J. , vol.11 , pp. 621-635
    • Mimura, M.1
  • 22
    • 0018830043 scopus 로고
    • Spatial segregation in competitive interaction-diffusion equations
    • M. Mimura, K. Kawasaki, Spatial segregation in competitive interaction-diffusion equations, J. Math. Biol. 9 (1990) 49-64.
    • (1990) J. Math. Biol. , vol.9 , pp. 49-64
    • Mimura, M.1    Kawasaki, K.2
  • 24
    • 0001637925 scopus 로고
    • Global existence of solutions for a strongly coupled quasilinear parabolic system
    • M.A. Pozio, A. Tesei, Global existence of solutions for a strongly coupled quasilinear parabolic system, Nonlinear Anal. 14 (1990) 657-689.
    • (1990) Nonlinear Anal. , vol.14 , pp. 657-689
    • Pozio, M.A.1    Tesei, A.2
  • 25
    • 0017340934 scopus 로고
    • Effects of diffusion on the stability of the equilibrium in multi-species ecological systems
    • G. Rosen, Effects of diffusion on the stability of the equilibrium in multi-species ecological systems, Bull. Math. Biol. 39 (1977) 373-383.
    • (1977) Bull. Math. Biol. , vol.39 , pp. 373-383
    • Rosen, G.1
  • 26
    • 0029690507 scopus 로고    scopus 로고
    • Positive steady-state solutions of a competing reaction-diffusion system with large cross-diffusion coefficients
    • W.H. Ruan, Positive steady-state solutions of a competing reaction-diffusion system with large cross-diffusion coefficients, J. Math. Anal. Appl. 197 (1996) 558-578.
    • (1996) J. Math. Anal. Appl. , vol.197 , pp. 558-578
    • Ruan, W.H.1
  • 27
    • 0000631186 scopus 로고
    • On the fixed point index and multiple steady-state solutions of reaction-diffusion systems
    • W.H. Ruan, W. Feng, On the fixed point index and multiple steady-state solutions of reaction-diffusion systems, Differential Integral Equations 8 (1995) 371-391.
    • (1995) Differential Integral Equations , vol.8 , pp. 371-391
    • Ruan, W.H.1    Feng, W.2
  • 29
    • 0003462525 scopus 로고
    • 2nd ed., Grundlehren der Mathematischen Wissenschaften, Springer, New York
    • J. Smoller, Shock Waves and Reaction-Diffusion Equations, 2nd ed., in: Grundlehren der Mathematischen Wissenschaften, Vol. 258, Springer, New York, 1994.
    • (1994) Shock Waves and Reaction-Diffusion Equations , vol.258
    • Smoller, J.1
  • 30
    • 0004326709 scopus 로고    scopus 로고
    • Existence of stationary solutions for a class of cross-diffusion systems with small parameters
    • Science Press, Beijing, to appear
    • Y.P. Wu, Existence of stationary solutions for a class of cross-diffusion systems with small parameters, in: Lecture Notes on Contemporary Mathematics, Science Press, Beijing, to appear.
    • Lecture Notes on Contemporary Mathematics
    • Wu, Y.P.1
  • 31
    • 0042062758 scopus 로고
    • Existence of positive solutions for semilinear elliptic system
    • (Trieste, 1990), School on Qualitative Aspects and Applications of Nonlinear Evolution Equations, World Scientific, River Edge, NJ
    • M. Wang, Z.Y. Li, Q.X. Ye, Existence of positive solutions for semilinear elliptic system, in: School on Qualitative Aspects and Applications of Nonlinear Evolution Equations (Trieste, 1990), World Scientific, River Edge, NJ, 1991, pp. 256-259.
    • (1991) , pp. 256-259
    • Wang, M.1    Li, Z.Y.2    Ye, Q.X.3
  • 32
    • 38248999657 scopus 로고
    • Global solution to some quasilinear parabolic system in population dynamics
    • A. Yagi, Global solution to some quasilinear parabolic system in population dynamics, Nonlinear Anal. 21 (1993) 603-630.
    • (1993) Nonlinear Anal. , vol.21 , pp. 603-630
    • Yagi, A.1


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