Dynamics of a single species in a fluctuating environment under periodic yield harvesting

We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sanchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameter sigma associated with the intensity of harvesting is explored. As sigma grows, the number of periodic solutions drops from two to zero. We provide bounds for the bifurcation parameter whose value in practice can be efficiently approximated numerically

Oscillation Theorems for Second-Order Nonlinear Neutral Delay Differential Equations

We analyze the oscillatory behavior of solutions to a class of second-order nonlinear neutral delay differential equations. Our theorems improve a number of related results reported in the literature

Asymptotic Behavior of Higher-Order Quasilinear Neutral Differential Equations

We study asymptotic behavior of solutions to a class of higher-order quasilinear neutral differential equations under the assumptions that allow applications to even- and odd-order differential equations with delayed and advanced arguments, as well as to functional differential equations with more complex arguments that may, for instance, alternate indefinitely between delayed and advanced types. New theorems extend a number of results reported in the literature. Illustrative examples are presented

Oscillation results for second-order nonlinear neutral differential equations

Published version of an article in the journal: Advances in Difference Equations. Also available from the publisher at: http://dx.doi.org/10.1186/1687-1847-2013-336 Open AccessWe obtain several oscillation criteria for a class of second-order nonlinear neutral differential equations. New theorems extend a number of related results reported in the literature and can be used in cases where known theorems fail to apply. Two illustrative examples are provided

Qualitative Theory of Differential Equations, Difference Equations, and Dynamic Equations on Time Scales

This issue on qualitative analysis on differential, fractional differential, and dynamic equations and related topics aims at an all-around research and the state-of-the-art theoretical, numerical, and practical achievements that contribute to this field

Oscillation of fourth-order quasilinear differential equations

summary:We study oscillatory behavior of a class of fourth-order quasilinear differential equations without imposing restrictive conditions on the deviated argument. This allows applications to functional differential equations with delayed and advanced arguments, and not only these. New theorems are based on a thorough analysis of possible behavior of nonoscillatory solutions; they complement and improve a number of results reported in the literature. Three illustrative examples are presented

Asymptotic behavior of an odd-order delay differential equation

Published version of an article in the journal: Boundary Value Problems. Also available from the publisher at: http://dx.doi.org/10.1186/1687-2770-2014-107 Open AccessWe study asymptotic behavior of solutions to a class of odd-order delay differential equations. Our theorems extend and complement a number of related results reported in the literature. An illustrative example is provided

Oscillatory behavior of second-order nonlinear neutral differential equations

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/143614 Open AccessWe study oscillatory behavior of solutions to a class of second-order nonlinear neutral differential equations under the assumptions that allow applications to differential equations with delayed and advanced arguments. New theorems do not need several restrictive assumptions required in related results reported in the literature. Several examples are provided to show that the results obtained are sharp even for second-order ordinary differential equations and improve related contributions to the subject