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How to solve Hammerstein equations. (English) Zbl 1156.45004
This note is a nice brief introduction to the theory of nonlinear Hammerstein integral equations which can be particularly useful to graduate students who are interested in nonlinear analysis. The authors briefly discuss the topological methods, monotonicity methods, variational methods and so called positivity methods. They also indicate some other techniques which can be applied to solve those equations. Example 1 in which applications of three fixed point theorems: the Banach contraction principle, the Schauder fixed point theorem, and the Vignioli one are compared, is interesting.

45G10 Other nonlinear integral equations
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
Full Text: DOI
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