메뉴 건너뛰기




Volumn 53, Issue 7-8, 2003, Pages 1115-1125

On positive solutions of the Lotka-Volterra cooperating models with diffusion

Author keywords

Lotka Volterra model; Periodic solution; Reaction diffusion system; Upper and lower solutions

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; ITERATIVE METHODS; MATHEMATICAL MODELS; REACTION KINETICS;

EID: 0037410103     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(03)00048-8     Document Type: Article
Times cited : (13)

References (30)
  • 1
    • 0001489777 scopus 로고
    • Asymptotic behavior of solutions of periodic competition diffusion system
    • Ahmad S., Lazer A.C. Asymptotic behavior of solutions of periodic competition diffusion system. Nonlinear Anal. 13:1989;263-284.
    • (1989) Nonlinear Anal. , vol.13 , pp. 263-284
    • Ahmad, S.1    Lazer, A.C.2
  • 2
    • 0001339498 scopus 로고
    • Global bifurcation of positive solutions in some systems of elliptic equations
    • Blat J., Brown K.J. Global bifurcation of positive solutions in some systems of elliptic equations. SIAM J. Math. Anal. 17:1985;1339-1353.
    • (1985) SIAM J. Math. Anal. , vol.17 , pp. 1339-1353
    • Blat, J.1    Brown, K.J.2
  • 3
    • 0001280950 scopus 로고
    • Positive periodic solutions of predator-prey reaction-diffusion systems
    • Brown K.J., Hess P. Positive periodic solutions of predator-prey reaction-diffusion systems. Nonlinear Anal. 16:1991;1147-1158.
    • (1991) Nonlinear Anal. , vol.16 , pp. 1147-1158
    • Brown, K.J.1    Hess, P.2
  • 4
    • 0001002603 scopus 로고
    • On positive solutions of some pairs of differential equations
    • Dancer E.N. On positive solutions of some pairs of differential equations. Trans. Am. Math. Soc. 284:1984;729-743.
    • (1984) Trans. Am. Math. Soc. , vol.284 , pp. 729-743
    • Dancer, E.N.1
  • 5
    • 84966251421 scopus 로고
    • On the existence and uniqueness of positive solutions for competing species models with diffusion
    • Dancer E.N. On the existence and uniqueness of positive solutions for competing species models with diffusion. Trans. Am. Math. Soc. 326:1991;829-859.
    • (1991) Trans. Am. Math. Soc. , vol.326 , pp. 829-859
    • Dancer, E.N.1
  • 6
    • 58149321092 scopus 로고
    • Positive solutions for a three-species competition system with diffusion-I. General existence results
    • Dancer E.N., Du Y. Positive solutions for a three-species competition system with diffusion-I. General existence results. Nonlinear Anal. 24:1995;337-357.
    • (1995) Nonlinear Anal. , vol.24 , pp. 337-357
    • Dancer, E.N.1    Du, Y.2
  • 7
    • 58149322315 scopus 로고
    • Positive solutions for a three-species competition system with diffusion-II. The case of equal birth rates
    • Dancer E.N., Du Y. Positive solutions for a three-species competition system with diffusion-II. The case of equal birth rates. Nonlinear Anal. 24:1995;359-373.
    • (1995) Nonlinear Anal. , vol.24 , pp. 359-373
    • Dancer, E.N.1    Du, Y.2
  • 8
    • 0003141001 scopus 로고    scopus 로고
    • ∞ estimates for a class of reaction-diffusion systems
    • ∞ estimates for a class of reaction-diffusion systems J. Math. Anal. Appl. 217:1998;72-94.
    • (1998) J. Math. Anal. Appl. , vol.217 , pp. 72-94
    • Dung, L.1
  • 9
    • 38248999812 scopus 로고
    • Coexistence, stability and limiting behavior in a one-predator-two-prey model
    • Feng W. Coexistence, stability and limiting behavior in a one-predator-two-prey model. J. Math. Anal. Appl. 179:1993;592-609.
    • (1993) J. Math. Anal. Appl. , vol.179 , pp. 592-609
    • Feng, W.1
  • 10
    • 0031126490 scopus 로고    scopus 로고
    • Existence of a global coexistence state for periodic competition diffusion systems
    • Fu S., Ma R. Existence of a global coexistence state for periodic competition diffusion systems. Nonlinear Anal. 28:1997;1265-1271.
    • (1997) Nonlinear Anal. , vol.28 , pp. 1265-1271
    • Fu, S.1    Ma, R.2
  • 11
    • 0003323485 scopus 로고
    • Periodic-parabolic boundary value problems and positivity
    • New York: Longman Scientific and Technical
    • Hess P. Periodic-parabolic Boundary Value Problems and Positivity. Pitman Research Notes in Mathematical Series. 247:1991;Longman Scientific and Technical, New York.
    • (1991) Pitman Research Notes in Mathematical Series , vol.247
    • Hess, P.1
  • 12
    • 0034747506 scopus 로고    scopus 로고
    • Global bifurcation and long time behavior of the Volterra-Lotka ecological model
    • Kaitai L., Lizhou W. Global bifurcation and long time behavior of the Volterra-Lotka ecological model. Internat. J. Bifurc. Chaos. 11:2001;133-142.
    • (2001) Internat. J. Bifurc. Chaos , vol.11 , pp. 133-142
    • Kaitai, L.1    Lizhou, W.2
  • 13
    • 0031106934 scopus 로고    scopus 로고
    • Instability of stationary solutions for a Lotka-Volterra competition model with diffusion
    • Kan-on Y. Instability of stationary solutions for a Lotka-Volterra competition model with diffusion. J. Math. Anal. Appl. 208:1997;158-170.
    • (1997) J. Math. Anal. Appl. , vol.208 , pp. 158-170
    • Kan-On, Y.1
  • 14
    • 0000716962 scopus 로고
    • On the existence and uniqueness of positive steady states in the Volterra-Lotka ecological models with diffusion
    • Korman P., Leung A. On the existence and uniqueness of positive steady states in the Volterra-Lotka ecological models with diffusion. Appl. Anal. 26:1987;145-160.
    • (1987) Appl. Anal. , vol.26 , pp. 145-160
    • Korman, P.1    Leung, A.2
  • 15
    • 0000154564 scopus 로고
    • Existence of steady-state solutions for a one-predator-two-prey system
    • Lakos N. Existence of steady-state solutions for a one-predator-two-prey system. SIAM J. Math. Anal. 21:1990;647-659.
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 647-659
    • Lakos, N.1
  • 16
    • 0020019093 scopus 로고
    • Monotone schemes for semilinear elliptic systems related to ecology
    • Leung A. Monotone schemes for semilinear elliptic systems related to ecology. Math. Methods Appl. Sci. 4:1982;272-285.
    • (1982) Math. Methods Appl. Sci. , vol.4 , pp. 272-285
    • Leung, A.1
  • 17
    • 0000495826 scopus 로고
    • A study of three species prey-predator reaction-diffusions by monotone schemes
    • Leung A. A study of three species prey-predator reaction-diffusions by monotone schemes. J. Math. Anal. Appl. 100:1984;583-604.
    • (1984) J. Math. Anal. Appl. , vol.100 , pp. 583-604
    • Leung, A.1
  • 18
    • 0000157645 scopus 로고    scopus 로고
    • Existence and monotone scheme for time-periodic nonquasimonotone reaction-diffusion systems: Application to autocatalytic chemistry
    • Leung L. Ortega A. Existence and monotone scheme for time-periodic nonquasimonotone reaction-diffusion systems. application to autocatalytic chemistry J. Math. Anal. Appl. 221:1998;712-733.
    • (1998) J. Math. Anal. Appl. , vol.221 , pp. 712-733
    • Leung, A.1    Ortega, L.2
  • 19
    • 0001508398 scopus 로고
    • Dynamics and numerical simulations of food-chain populations
    • Lu X., Feng W. Dynamics and numerical simulations of food-chain populations. Appl. Math. Comput. 65:1994;335-344.
    • (1994) Appl. Math. Comput. , vol.65 , pp. 335-344
    • Lu, X.1    Feng, W.2
  • 20
    • 0002902529 scopus 로고
    • Coexistence and stability of a competition-diffusion system in population dynamics
    • Pao C.V. Coexistence and stability of a competition-diffusion system in population dynamics. J. Math. Anal. Appl. 83:1981;54-76.
    • (1981) J. Math. Anal. Appl. , vol.83 , pp. 54-76
    • Pao, C.V.1
  • 21
    • 0020136496 scopus 로고
    • On nonlinear reaction-diffusion systems
    • Pao C.V. On nonlinear reaction-diffusion systems. J. Math. Anal. Appl. 87:1982;165-198.
    • (1982) J. Math. Anal. Appl. , vol.87 , pp. 165-198
    • Pao, C.V.1
  • 23
    • 0030174199 scopus 로고    scopus 로고
    • Quasisolution and global attractor of reaction-diffusion systems
    • Pao C.V. Quasisolution and global attractor of reaction-diffusion systems. Nonlinear Anal. 26:1996;1889-1903.
    • (1996) Nonlinear Anal. , vol.26 , pp. 1889-1903
    • Pao, C.V.1
  • 24
    • 0001592706 scopus 로고    scopus 로고
    • Parabolic systems in unbounded domains I. Existence and dynamics
    • Pao C.V. Parabolic systems in unbounded domains I. Existence and dynamics. J. Math. Anal. Appl. 217:1998;129-160.
    • (1998) J. Math. Anal. Appl. , vol.217 , pp. 129-160
    • Pao, C.V.1
  • 25
    • 0001592705 scopus 로고    scopus 로고
    • Parabolic systems in unbounded domains II. Equations with time delays
    • Pao C.V. Parabolic systems in unbounded domains II. Equations with time delays. J. Math. Anal. Appl. 225:1998;557-586.
    • (1998) J. Math. Anal. Appl. , vol.225 , pp. 557-586
    • Pao, C.V.1
  • 26
    • 0000919241 scopus 로고    scopus 로고
    • Periodic solutions of parabolic systems with nonlinear boundary conditions
    • Pao C.V. Periodic solutions of parabolic systems with nonlinear boundary conditions. J. Math. Anal. Appl. 234:1999;695-716.
    • (1999) J. Math. Anal. Appl. , vol.234 , pp. 695-716
    • Pao, C.V.1
  • 27
    • 0034172560 scopus 로고    scopus 로고
    • Periodic solutions of systems of parabolic equations in unbounded domains
    • Pao C.V. Periodic solutions of systems of parabolic equations in unbounded domains. Nonlinear Anal. 40:2000;523-535.
    • (2000) Nonlinear Anal. , vol.40 , pp. 523-535
    • Pao, C.V.1
  • 28
    • 0000749761 scopus 로고
    • Existence of global coexistence state for periodic competition diffusion systems
    • Tineo A. Existence of global coexistence state for periodic competition diffusion systems. Nonlinear Anal. 19:1992;335-344.
    • (1992) Nonlinear Anal. , vol.19 , pp. 335-344
    • Tineo, A.1
  • 29
    • 0001355473 scopus 로고
    • Asymptotic behavior of solutions of a periodic reaction-diffusion system of a competitor-competitor-mutualist model
    • Tineo A. Asymptotic behavior of solutions of a periodic reaction-diffusion system of a competitor-competitor-mutualist model. J. Differential Equations. 108:1994;326-341.
    • (1994) J. Differential Equations , vol.108 , pp. 326-341
    • Tineo, A.1
  • 30
    • 0000211242 scopus 로고
    • Asymptotic behavior of a competition-diffusion system in population dynamics
    • Zhou L., Pao C.V. Asymptotic behavior of a competition-diffusion system in population dynamics. Nonlinear Anal. 6:1982;1163-1184.
    • (1982) Nonlinear Anal. , vol.6 , pp. 1163-1184
    • Zhou, L.1    Pao, C.V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.