Abstract
In this paper we study the quadratic integral equation of the form
We discuss the existence of solutions for the above equation in different function spaces. We stress on the case when f has non-polynomial growth which leads to solutions in Orlicz spaces. The detailed theory for a wide class of spaces is presented. Some existence theorems for a.e. monotonic solutions in Orlicz spaces are proved either for strongly nonlinear functions f or for rapidly growing kernel K. The presented method allows us to extend the current results as well as to unify the proofs for both quadratic and non-quadratic cases.
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Cichoń, M., Metwali, M.M.A. On Solutions of Quadratic Integral Equations in Orlicz Spaces. Mediterr. J. Math. 12, 901–920 (2015). https://doi.org/10.1007/s00009-014-0450-x
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DOI: https://doi.org/10.1007/s00009-014-0450-x