On Periodic Solutions of Higher-Order Functional Differential Equations

For higher-order functional differential equations and, particularly, for nonautonomous differential equations with deviated arguments, new sufficient conditions for the existence and uniqueness of a periodic solution are established

The dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations

summary:The a priori boundedness principle is proved for the Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations. Several sufficient conditions of solvability of the Dirichlet problem under consideration are derived from the a priori boundedness principle. The proof of the a priori boundedness principle is based on the Agarwal-Kiguradze type theorems, which guarantee the existence of the Fredholm property for strongly singular higher-order linear differential equations with argument deviations under the two-point conjugate and right-focal boundary conditions

Behaviour and Population Dynamics of Entomopathogenic Nematodes Following Application

Entomopathogenic nematodes (EPN) of the genera Steinernema and Heterorhabditis are widely used in inundative biological pest control programmes. It has long been recognised that increased understanding of the ecology of EPN is important for better predictions of field performance and environmental risk (Ehlers & Hokkanen, 1996; Gaugler, Lewis, & Stuart, 1997). Increasingly, EPN are also finding a place as model organisms for fundamental studies in behavioural ecology and evolutionary biology (Campos-Herrera, Barbercheck, Hoy, & Stock, 2012). In this chapter, I consider the fate of EPN used in biocontrol, focussing largely on inundative application to soil. The aim is to provide an overview of the transformation of a biotechnological product to an ecological entity, rather than a review of this rather broad topic. There are already several extensive reviews relevant to the subject, including EPN behaviour and their fate in soil (e.g. Griffin, 2012; Kaya, 2002; Lewis, Campbell, Griffin, Kaya, & Peters, 2006; Stuart, Barbercheck, Grewal, Taylor, & Hoy, 2006; see also Chap. 4). It should be noted that, while the concept of this chapter is to follow the fate of commercially produced EPN when applied to soil, many of the laboratory studies cited have used nematodes produced in insects rather than taken from commercial formulations