JournalszaaVol. 14, No. 2pp. 285–325

Some Results on Non-Coercive Variational Problems and Applications

  • F. Weissbaum

    Ecole Polytechnique Federale, Lausanne, Switzerland
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Abstract

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 uu we consider are lipschitz functions, i.e. uW1,(0,1)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 u0u' ≥ 0 and finally a problem with u0u ≥ 0. 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. 285–325

DOI 10.4171/ZAA/676