J. Aubin and I. Ekeland, Applied nonlinear analysis, 1984.

M. Bachir and J. , Blot Infinite Dimensional Infinite-horizon Pontryagin principles for discrete-time problems, Set-Valued Var, Anal, vol.23, pp.43-54, 2015.
DOI : 10.1007/s11228-014-0302-7

M. Bachir and J. , Blot Infinite dimensional multipliers and Pontryagin principles for discretetime problems, Pure and Applied Functional Analysis
DOI : 10.1007/s11228-014-0302-7

J. Blot and P. Cieutat, Completness of sums of subspaces of bounded functions and applications, Commun. Math. Anal, vol.19, issue.2, pp.43-61, 2018.

J. Blot and H. Chebbi, Discrete Time Pontryagin Principles with Infinite Horizon, Journal of Mathematical Analysis and Applications, vol.246, issue.1, pp.265-279, 2000.
DOI : 10.1006/jmaa.2000.6797
URL : http://doi.org/10.1006/jmaa.2000.6797

J. Blot and N. Hayek, Infinite-horizon optimal control in the discrete-time framework
DOI : 10.1007/978-1-4614-9038-8

D. A. Carlson, A. B. Haurie, and A. Leizarowitz, Infinite horizon optimal control; deterministic and stochastic systems, Second revised edition, 1991.

W. C. Clark, Mathematical bioeconomics; optimal management of renewable resources, second edition, 2005.

J. Jahn, Introduction to the theory of nonlinear optimization, 2007.
DOI : 10.1007/978-3-662-03271-8

P. Michel, Some Clarifications on the Transversality Condition, Econometrica, vol.58, issue.3, pp.705-728, 1990.
DOI : 10.2307/2938197

N. L. Stokey, R. E. Lucas, and E. C. Prescott, Recursive methods in economic dynamics, 1989.

A. J. Zaslavski, Turnpike properties in the calculus of variations and optimal Control, 2006.

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