Uniqueness of the optimal control for a Lotka-Volterra control problem with a large crowding effect
ESAIM: Control, Optimisation and Calculus of Variations, Tome 2 (1997), pp. 1-12.
@article{COCV_1997__2__1_0,
     author = {G\'amez, J. L. and Montero, J. A.},
     title = {Uniqueness of the optimal control for a {Lotka-Volterra} control problem with a large crowding effect},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1--12},
     publisher = {EDP-Sciences},
     volume = {2},
     year = {1997},
     mrnumber = {1440076},
     zbl = {0868.49004},
     language = {en},
     url = {http://archive.numdam.org/item/COCV_1997__2__1_0/}
}
TY  - JOUR
AU  - Gámez, J. L.
AU  - Montero, J. A.
TI  - Uniqueness of the optimal control for a Lotka-Volterra control problem with a large crowding effect
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 1997
SP  - 1
EP  - 12
VL  - 2
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/COCV_1997__2__1_0/
LA  - en
ID  - COCV_1997__2__1_0
ER  - 
%0 Journal Article
%A Gámez, J. L.
%A Montero, J. A.
%T Uniqueness of the optimal control for a Lotka-Volterra control problem with a large crowding effect
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 1997
%P 1-12
%V 2
%I EDP-Sciences
%U http://archive.numdam.org/item/COCV_1997__2__1_0/
%G en
%F COCV_1997__2__1_0
Gámez, J. L.; Montero, J. A. Uniqueness of the optimal control for a Lotka-Volterra control problem with a large crowding effect. ESAIM: Control, Optimisation and Calculus of Variations, Tome 2 (1997), pp. 1-12. http://archive.numdam.org/item/COCV_1997__2__1_0/

[1] H. Amann: Fixed points equations and nonlinear eigenvalue problems in ordered banach spaces, SIAM review, 18, 4, October 1976, 620-709. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[7] P. Hess: Periodic-parabolic boundary value problems and posuivity, Longman Group U.K. Limited, 1991. | MR | Zbl

[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. | MR | Zbl

[9] A. Leung: Systems of nonlinear partial differential equations, The Netherlands, Kluwer Acacemic Publishers, 1989. | MR | Zbl

[10] A. Leung and S. Stojanovic: Direct methods for some distributed games, Diff. and Int. Eqns., 3, 1990, 1113-1125. | MR | Zbl

[11] A. Leung and S. Stojanovic: Optimal control for elliptic Volterra-Lotka equations, J. Math. Anal. Appl., 173 1993, 603-619. | MR | Zbl

[12] L. Li and R. Logan: Positive solutions to general elliptic competition models, Diff. and Int. Eqns., 4, 1991, 817-834. | MR | Zbl

[13] S. Stojanovic: Optimal damping control and nonlinear elliptic Systems, SIAM J. Control Optim., 29, 1991, 594-608. | MR | Zbl

[14] J. Smoller: Shock waves and reaction-diffusion equations, NewYork, Springer, 1983. | MR | Zbl