Some Results on Non-Coercive Variational Problems and Applications (original) (raw)

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. tz E W"-(O, 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 v' 0 and finally a problem with u 0. These problems can be related to optimal foraging models in behavioural ecology.