On nonlinear integro-differential operators in generalized Orlicz-Sobolev spaces

A nonlinear integral operator T of the form (Tf)(s) = integral(G) K(t, f(sigma(s, t))) d mu(t), for s is an element of G, is defined and investigated in the measure space (G, Sigma, mu), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz-Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T. (C) 2000 Academic Press.