# Optimal Harvesting in a Periodic Food Chain Model with Size Structures in Predators

Optimal Harvesting in a Periodic Food Chain Model with Size Structures in Predators In this paper, we investigate a periodic food chain model with harvesting, where the predators have size structures and are described by first-order partial differential equations. First, we establish the existence of a unique non-negative solution by using the Banach fixed point theorem. Then, we provide optimality conditions by means of normal cone and adjoint system. Finally, we derive the existence of an optimal strategy by means of Ekeland’s variational principle. Here the objective functional represents the net economic benefit yielded from harvesting. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Optimal Harvesting in a Periodic Food Chain Model with Size Structures in Predators

, Volume 75 (2) – Jan 30, 2016
23 pages

/lp/springer_journal/optimal-harvesting-in-a-periodic-food-chain-model-with-size-structures-BSZSiwKPWJ
Publisher
Springer US
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-016-9331-y
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we investigate a periodic food chain model with harvesting, where the predators have size structures and are described by first-order partial differential equations. First, we establish the existence of a unique non-negative solution by using the Banach fixed point theorem. Then, we provide optimality conditions by means of normal cone and adjoint system. Finally, we derive the existence of an optimal strategy by means of Ekeland’s variational principle. Here the objective functional represents the net economic benefit yielded from harvesting.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 30, 2016

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