EXISTENCE OF SOLUTIONS FOR A VARIATIONAL PROBLEM ASSOCIATED TO MODELS IN OPTIMAL FORAGING THEORY

Realistic extensions of a model by R. Arditi and B. Dacorogna (1985, Math. Biosci. 76, 127-145) in optimal foraging theory are considered. Mathematically, they correspond to minimization problems (in the calculus of variations) of convex but not coercive functionals: E(v) = ∝ g(x, v′) dx with prescribed boundary conditions and v′ ≥ β ≥ 0. Existence, uniqueness, and characterization of solutions are given. The limits of the result are discussed, in particular the case with dependence on v: g = g(x, v, v′). © 1990.