In this paper we study a class of multivalued Neumann boundary problem governed by the general p(.)-Leray-Lions type operator and involving a natural growth term and L1 data. Using the technique of maximal monotone operator in Banach spaces and the approximation method via Yosida regularisation and penalizing term, we firstly prove the existence of at least one weak solution when the right hand side datum is bounded. Secondly, we deduce the existence of at least one renormalized solution when the right and side datum belongs in L1. By choosing an appropriate test function, we end by establishing a relationship between renormalized solution and the entropy one.

Generalized Lebesgue-Sobolev spaces, Leray-Lions type operator, Yosida regularisation, maximal monotone graph