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Zeitschrift für Analysis und ihre Anwendungen

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Volume 14, Issue 2, 1995, pp. 285–325
DOI: 10.4171/ZAA/676

Published online: 1995-06-30

Some Results on Non-Coercive Variational Problems and Applications

F. Weissbaum[1]

(1) Ecole Polytechnique Federale, Lausanne, Switzerland

We give a necessary and sufficient condition to ensure the existence of solutions of three problems of the calculus of variations with non-coercive integrands. The solutions $u$ we consider are lipschitz functions, i.e. $u \in W^{1, \infty} (0,1)$. The three problems depends on the same functionals but are different in the constraints. We consider respectively a problem without constraint, a problem with $u' ≥ 0$ and finally a problem with $u ≥ 0$. These problems can be related to optimal foraging models in behavioural ecology.

Keywords: Calculus of variations, convexity, non-coercive and constraint problems

Weissbaum F.: Some Results on Non-Coercive Variational Problems and Applications. Z. Anal. Anwend. 14 (1995), 285-325. doi: 10.4171/ZAA/676