Methods in Nonlinear Integral Equations presents several extremely
fruitful methods for the analysis of systems and nonlinear integral
equations. They include: fixed point methods (the Schauder and
Leray-Schauder principles), variational methods (direct variational
methods and mountain pass theorems), and iterative methods (the
discrete continuation principle, upper and lower solutions
techniques, Newton's method and the generalized quasilinearization
method). Many important applications for several classes of
integral equations and, in particular, for initial and boundary
value problems, are presented to complement the theory. Special
attention is paid to the existence and localization of solutions in
bounded domains such as balls and order intervals. The presentation
is essentially self-contained and leads the reader from classical
concepts to current ideas and methods of nonlinear analysis.
This work will be of interest to graduate students and theoretical
and applied mathematicians in nonlinear functional analysis,
integral equations, ordinary and partial differential equations,
and related fields.
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