Uniqueness of the optimal control for a lotka-volterra control problem with a large crowding effect

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 2, Issue , 1997, Pages 1-12

  Gamez J L ^a   Montero, J A ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347510071     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:1997100     Document Type: Article

References (14)

1. H. Amann: Fixed points equations and nonlinear eigenvalue problems in ordered banach spaces, SIAM review, 18, 4, October 1976, 620-709.
2. H. Berestycki and P.L. Lions: Some applications of the method of super and subsolutions, Lect. Not. Math., 782, Springer-Verlag, 1980, 16-42.
3. J. Blat and K.J. Brown: Bifurcation of steady-state solutions in predator-prey and competition systems, Proc. of the Roy. Soc. Edinburg, 97, 1984, 21-34.
4. A. Cañada, J.L. Gámez and J.A. Montero: An optimal control problem for a nonlinear elliptic equation arising from population dynamics, in Calculus of Variation, Applications and Computations, Longman, Pitman Research Notes in Mathematics Series, C. Bandle, J. Bemelmans, M. Chipot, J. Saint Jean Paulin and I. Shafrir, editors, 326, 1995, 35-40.
5. A. Cañada, J.L. Gámez and J.A. Montero: Study of a nonlinear optimal control problem for diffusive Volterra-Lotka equations, to appear.
6. D. Gilbarg and N.S. Trudinger: Elliptic Partial Differential Equations of Second Order, 2nd Edition, Springer-Verlag, Berlin, 1983.
7. P. Hess: Periodic-parabolic boundary value problems and positivity, Longman Group U.K. Limited, 1991.
8. F. He, A. Leung and S. Stojanovic: Periodic optimal control for parabolic Volterra-Lotka type equations, Math. Methods Appl. Sci., 18, 1995, 127-146.
9. A. Leung: Systems of nonlinear partial differential equations, The Netherlands, Kluwer Acacemic Publishers, 1989.
10. A. Leung and S. Stojanovic: Direct methods for some distributed games, Diff. and Int. Eqns., 3, 1990, 1113-1125.
11. A. Leung and S. Stojanovic: Optimal control for elliptic Volterra-Lotka equations, J. Math. Anal. Appl., 173, 1993, 603-619.
12. L. Li and R. Logan: Positive solutions to general elliptic competition models, Diff. and Int. Eqns., 4, 1991, 817-834.
13. S. Stojanovic: Optimal damping control and nonlinear elliptic systems, SIAM J. Control Optim., 29, 1991, 594-608.
14. J. Smoller: Shock waves and reaction-diffusion equations, New York, Springer, 1983.