Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/optimal-control-for-the-degenerate-elliptic-logistic-equation-ZqfyQasy1k
References (11)
-
M. Delgado, A. Suárez (2000)
On the existence of dead cores for degenerate Lotka—Volterra modelsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 130
-
H. Amann (1976)
Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach SpacesSiam Review, 18
-
A. Brodsky, M. Krasnoselskii, Richard Flaherty, L. Boron (1964)
Positive solutions of operator equations -
A. Leung (1995)
Optimal harvesting-coefficient control of steady-state prey-predator diffusive Volterra-Lotka systemsApplied Mathematics and Optimization, 31
-
O. Kavian (1993)
Introduction à la théorie des points critiques : et applications aux problèmes elliptiques -
A. Cañada, J. Gámez, J. Montero (1998)
Study of an optimal control problem for diffusive nonlinear elliptic equations of logistic typeProceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), 3
-
J. Montero (2000)
A Uniqueness Result for an Optimal Control Problem on a Diffusive Elliptic Volterra–Lotka Type Equation☆Journal of Mathematical Analysis and Applications, 243
-
A. Leung, S. Stojanovic (1993)
Optimal Control for Elliptic Volterra-Lotka Type EquationsJournal of Mathematical Analysis and Applications, 173
-
A. Kufner (1985)
Weighted Sobolev Spaces -
M. Gurtin, R. MacCamy (1977)
On the diffusion of biological populationsBellman Prize in Mathematical Biosciences, 33
-
M. Bertsch, R. Rostamian (1985)
The principle of linearized stability for a class of degenerate diffusion equationsJournal of Differential Equations, 57
- Publisher
- Springer Journals
- Copyright
- Copyright © Inc. by 2002 Springer-Verlag New York
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-001-0039-1
- Publisher site
- See Article on Publisher Site
Abstract
We consider the optimal control of harvesting the diffusive degenerate elliptic logistic equation. Under certain assumptions, we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the optimal control are also derived. The sub-supersolution method, the singular eigenvalue problem and differentiability with respect to the positive cone are the techniques used to obtain our results.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Jun 5, 2002