On nonlinear integro-differential operators in generalized Orlicz-Sobolev spaces (Q1583969)

A nonlinear integral operator \(T\) of the form \[ (Tf)(s)= \int_G K(t, f(\sigma(s,t))) d\mu(t) \] is investigated, where \(\sigma: G\times G\to G\), \(f: G\to E\), \(K: G\times E\to F\), \(E\) and \(F\) are normed linear spaces. As an application there are obtained results concerning problems of existence, embedding and approximation for functions from Orlicz-Sobolev spaces by means of operators \(T\) of the above form.