Positive steady-state solutions of a non-linear reaction-diffusion system

Mathematical Methods in the Applied Sciences

Volumn 20, Issue 7, 1997, Pages 625-634

  Chen, Hongwei ^a  

^a CHRISTOPHER NEWPORT UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; NONLINEAR EQUATIONS; NONLINEAR SYSTEMS; PROBLEM SOLVING; THEOREM PROVING;

FIXED POINT THEOREM; ORDERED BANACH SPACES; REACTION DIFFUSION SYSTEMS; STEADY STATE PROBLEMS;

BOUNDARY VALUE PROBLEMS;

EID: 6944255272     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(19970510)20:7<625::AID-MMA873>3.0.CO;2-V     Document Type: Article

References (14)

1. Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev., 18, 620-709 (1976).
2. Chen, Hongwei, 'Blow-up of solutions for nonlinear parabolic boundary value problems', Ph. D Thesis, North Carolina State University, June 1991.
3. Dancer, E. N., 'On the existence and uniqueness of positive solutions for competing species with diffusion', Trans. Amer. Math. Soc., 326, 829-859 (1981).
4. Dancer, E.N., 'On positive solutions of some pair of differential equations I', Trans. Amer. Math. Soc., 284, 729-743 (1984).
5. Dancer, E. N. 'On positive solutions of some pair of differntial equations II', J. Diff. Eqs., 60, 236-258 (1985).
6. Gidas, B., Ni, W. M. and Nirenberg, L., 'Symmetry and related properties via the maximum principle', Comm. Math. Phys., 68, 209-243 (1979).
7. Kastenberg, W.E. and Chamber, P.L. 'On the stability of non-linear space-dependent reactor kinetics', Nuclear Sci. Eng., 31, 67-79 (1968).
8. Li, L., 'On positive solutions of a nonlinear equilibrium boundary value problem', J. Math. Anal. Appl., 138, 537-549 (1989).
9. Li, L., and Logan, R., 'Positive solutions to general elliptic competition models', Differential Integral Eqs., 4, 817-834 (1991).
10. Ni, W. M., Sacks, P. E. and Tavantzis, J. 'On the asymptotic behavior of solutions of certain quasilinear parabolic equations', J. Diff. Eqs., 54, 97-120 (1984).
11. Pao, C. V. 'Bifurcation analysis on a nonlinear diffusion system in reactor dynamics' J. Appl. Anal., 9, 107-119 (1979).
12. Pao, C. V. 'On nonlinear reaction-diffusion systems', J. Math. Anal. Anal., 87, 165-198 (1982).
13. Pao, C. V. 'Nonlinear Parabolic and Elliptic Equations, Plenum, New York, 1992.
14. Stacey, W. M., Jr., Space-Time Nuclear Reactor Kinetics, Academic Press, New York, 1969.