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Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models. During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.

Boundary value problems. --- Differential equations. --- Prediction theory. --- Stochastic processes. --- Random processes --- Probabilities --- Forecasting theory --- Stochastic processes --- 517.91 Differential equations --- Differential equations --- Boundary conditions (Differential equations) --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Boundary Value Problem. --- Condensing. --- Contraction. --- Controllability. --- Differential Inclusion. --- Filippov's Theorem. --- Hyperbolic Differential Inclusion. --- Impulsive Functional Differential Equation. --- Infinite Delay. --- Normal Cone. --- Relaxation. --- Seeping Process. --- Stability. --- Stochastic Differential Equation. --- Variable Times. --- Viable Solution.

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This book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied to study the existence of two or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowflies model, and some models with Allee effects. Many interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the global appeal of solutions to the models considered in the earlier chapters. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students and researchers in the field of differential equations with applications to biology, ecology, and the environment.

Population --- Differential equations --- Mathematical models. --- Asymptotic theory. --- 517.91 Differential equations --- Differential Equations. --- Global analysis (Mathematics). --- Integral equations. --- Ordinary Differential Equations. --- Analysis. --- Mathematical and Computational Biology. --- Integral Equations. --- Equations, Integral --- Functional equations --- Functional analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Differential equations. --- Mathematical analysis. --- Analysis (Mathematics). --- Biomathematics. --- Biology --- Mathematics --- 517.1 Mathematical analysis --- Mathematical analysis

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This book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied to study the existence of two or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowflies model, and some models with Allee effects. Many interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the global appeal of solutions to the models considered in the earlier chapters. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students and researchers in the field of differential equations with applications to biology, ecology, and the environment.

Algebra --- Differential geometry. Global analysis --- Differential equations --- Mathematical analysis --- Mathematics --- Biology --- Computer science --- differentiaalvergelijkingen --- algebra --- analyse (wiskunde) --- biologie --- informatica --- statistiek --- wiskunde

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This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019. First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. The book includes studies on boundary value problems; Markov models; time scales; non-linear difference equations; multi-scale modeling; and myriad applications.

Operator theory --- Functional analysis --- Partial differential equations --- Differential equations --- Numerical analysis --- differentiaalvergelijkingen --- analyse (wiskunde) --- mathematische modellen --- numerieke analyse