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 we consider are lipschitz functions, i.e. . The three problems depends on the same functionals but are different in the constraints. We consider respectively a problem without constraint, a problem with and finally a problem with . These problems can be related to optimal foraging models in behavioural ecology.
Cite this article
F. Weissbaum, Some Results on Non-Coercive Variational Problems and Applications. Z. Anal. Anwend. 14 (1995), no. 2, pp. 285–325DOI 10.4171/ZAA/676