Serena Matucci

A problem of optimal harvesting policy in two-stage age-dependent populations

The optimal equilibrium harvesting policy is investigated for an age-dependent population of females whose life history consists of two stages termed eggs (or juveniles) and adults. Using a continuous-time linear model, we consider admissible harvesting policies in which a certain fraction of individuals of fixed ages is harvested per unit time in both stages to bring the population to an equilibrium level. Determination of the harvest rate that maximizes the sustainable yield, subject to a linear ecological or economic constraint, leads to a nonlinear, nonconvex optimization problem. The optimal policy is shown to consist of harvesting at most three ages. Thus, we say that the harvest is trimodal. In one stage, at most two ages are harvested, with the oldest being harvested completely; in the other, at most one age is harvested completely. In each stage, the age totally removed, if present, is older than the surplus age, which is the age at which the proportion of the expected number of eggs multiplied by the proportion of the expected number of adults first exceeds one. The three harvesting ages are dependent on the birth, maturation, and death rates and on the economic parameters of the problem. A simple algorithm to find the optimum harvesting strategy is described.

Regularly varying sequences and second order difference equations

Some basic properties of regularly varying sequences are presented here and applied to the study of the asymptotic behavior of decreasing solutions of half-linear difference equations. Relations with the classification of nonoscillatory solutions and with the notion of recessive solutions are also discussed.

Rapidly varying decreasing solutions of half-linear difference equations

In this paper a necessary and sufficient condition is derived for all positive decreasing solutions of a half-linear second order difference equation to be rapidly varying of index -~. Relations with the standard classification of nonoscillatory solutions and with the notion of recessive solutions are also discussed. The results of this paper are complementary to those of a previous paper by the authors, and lead to a complete characterization of positive decreasing solutions with respect to their regularly or rapidly varying behavior.

Regularly Varying Solutions of Second-Order Difference Equations with Arbitrary Sign Coefficient

Necessary and sufficient conditions for regular or slow variation of all positive solutions of a second-order linear difference equation with arbitrary sign coefficient are established. Relations with the so-called -classification are also analyzed and a generalization of the results to the half-linear case completes the paper.

Boundary value problems for functional difference equations on infinite intervals

A general method for solving boundary value problems associated to functional difference systems on the discrete half-line is presented and applied in studying the existence of positive unbounded solutions for a system of two coupled nonlinear difference equations. A further example, illustrating the method, completes the paper.

Nonoscillatory solutions of a second-order nonlinear discrete system

A complete characterization for nonoscillatory solutions of a coupled nonlinear difference system is presented. Nonoscillatory solutions are classified into several classes according to their limit behavior, and necessary and sufficient conditions for the existence in each of these classes are established. The multiplicity of solutions is also examined and explicit asymptotic formulas are derived. Possible generalizations and comparisons of our results with existing ones are discussed as well.

Necessary and sufficient conditions for oscillation of coupled nonlinear discrete systems

Je dokazan novy vysledek tykajici se oscilace nelinearniho diferencniho systemu dvou rovnic druheho radu, ktery kompletuje predchozi vysledky autoru. Dostava se takto kompletni charakterizace oscilace pro tuto tridu systemu.

Positive decaying solutions to BVPs with mean curvature operator

A nonlocal boundary value problem on the half-closed interval, associated to differential equations with the Euclidean mean curvature operator or with the Minkowski mean curvature operator is here considered. By using a new approach, based on a linearization device and some properties of principal solutions of certain disconjugate second-order linear equations, the existence of global positive decaying solutions is examined.

Decaying solutions for discrete boundary value problems on the half line

Some nonlocal boundary value problems, associated to a class of functional difference equations on unbounded domains, are considered by means of a new approach. Their solvability is obtained by using properties of the recessive solution to suitable half-linear difference equations, a half-linearization technique and a fixed point theorem in Frechét spaces. The result is applied to derive the existence of nonoscillatory solutions with initial and final data. Examples and open problems complete the paper.