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'ski? 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, Caratheodory 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.
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