Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap.The systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically.The existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo–Krasnosel'skiĭ fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Carathéodory functions, and sequences. Moreover, the final part in the volume features some techniques on how to relate differential coupled systems to integral ones, which require less regularity.Parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on physics, mechanics, biology, forestry, and dynamical systems, which researchers and students will find useful.
Contents: - Boundary Value Problems on Bounded Domains:
- Third-Order Three Point Systems with Dependence on the First Derivative
- Functional Coupled Systems with Full Nonlinear Terms
- Coupled Systems on Unbounded Domains:
- Second-Order Coupled Systems on the Half-Line
- Homoclinic Solutions for Second-Order Coupled Systems
- Heteroclinic Solutions with Phi-Laplacians
- Coupled Impulsive Systems:
- Impulsive Coupled Systems with Generalized Jump Conditions
- Impulsive Coupled Systems on the Half-Line
- Localization Results for Impulsive Second-Order Coupled Systems on the Half-Line
- Coupled Systems of Integral Equations:
- Coupled Systems of Hammerstein Integral Equations
- Coupled Hammerstein Systems with Sign-Changing Kernels
- Generalized Hammerstein Coupled Systems on the Real Line
Readership: Academics, researchers and graduate students on Mathematics or related fields such as Engineering who are interested in coupled systems of differential and integral equations. Coupled Systems;Green Functions;Guo–Krasnosel'skiĭ Fixed-Point in Cones;Functional Boundary Conditions;Schauder's Fixed-Point Theorem;Lower and Upper Solutions;Problems on the Half-Line;Equation on the Real Line;Impulsive Coupled Systems;Heteroclinic and Homoclinic Solutions;Hammerstein Integral Equations;Kernels Functions;Sign Changing Kernels;Arzelà–Ascoli Theorem;Homeomorphism;Operator Theory;L1-Carathéodory Functions;Equiconvergence at Infinity;Equiconvergence at Impulsive Points;Truncature Technique;Coupled Mass-spring System;Elastically Coupled Double-String System;L1-Carathéodory Sequences;Bending of Suspension Bridges;Infinite Beams0
Key Features:- This book is unique where the reader can find sufficient conditions for the solvability of: Functional coupled systems; Homoclinic and heteroclinic solutions for coupled systems; Impulsive coupled systems with generalized impulsive conditions on finite or infinite time; Integral Hammerstein integral equations, allowing kernel functions to change sign on bounded or unbounded domains
