Ricerche mat. DOI 10.1007/s11587-017-0322-3 Existence of renormalized solution of nonlinear elliptic problems with lower order term in Orlicz spaces H. Moussa 1 · M. Rhoudaf 1 Received: 18 June 2016 / Revised: 8 March 2017 © Università degli Studi di Napoli "Federico II" 2017 Abstract In this paper, we shall be concerned with the existence of renormalized solution of the following problem,  −div  a(x , u , ∇u )  − div((x , u )) = f in , u = 0 on ∂, with the second term f belongs to L 1 (). The growth and the coercivity conditions on the monotone vector field a are prescribed by a N -function M . We assume any restriction on M , therefore we work with Orlicz-Sobolev spaces which are not nec- essarily reflexive. The lower order term  is a Carathéodory function which is not coercive. Keywords Nonlinear elliptic problems · Non-polynomial growth · Orlicz-Sobolev spaces · Renormalized solutions · Lower order terms Mathematics Subject Classification 35J60 · 35D99 · 35B45 1 Introduction In recent years, there has been an increasing interest in the study of various mathemat- ical problems involving the operators satisfying non-polynomial growth conditions B H. Moussa hichammoussa23@gmail.com M. Rhoudaf rhoudafmohamed@gmail.com 1 Département Mathématiques, Faculté des Sciences Meknés, Université Moulay Ismail, Meknes, Morocco 123