Ricerche mat. DOI 10.1007/s11587-017-0342-z Existence result for nonlinear elliptic unilateral problems in Musielak framework with L 1 data Mustafa Ait Khellou 1 · Sidi Mohamed Douiri 2 · Youssef El Hadfi 3 Received: 13 April 2017 / Revised: 13 October 2017 © Università degli Studi di Napoli "Federico II" 2017 Abstract We give an existence result for nonlinear elliptic unilateral problems having natural growth terms and L 1 data in Musielak–Orlicz spaces. Keywords Musielak–Orlicz spaces · Nonlinear problems · Unilateral problems · Truncations Mathematics Subject Classification 35J87 1 Introduction Let Ω be an open bounded subset of R N ( N ≥ 2). Consider the following non-linear Dirichlet problem A(u ) + g(x , u , ∇u ) = f , (1) B Mustafa Ait Khellou maitkhellou@gmail.com Sidi Mohamed Douiri douiri.s.m@gmail.com Youssef El Hadfi yelhadfi@gmail.com 1 Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University of Fez, P.O. Box 1796, Atlas, 30000 Fez, Morocco 2 Department of Mathematics (AMNEA Group), Faculty of Sciences and Technics, Moulay Ismail University, P.O. Box 509, Boutalamine, Errachidia 52000, Morocco 3 Laboratory LIPOSI, National School of Applied Sciences, University Hassan 1, 25000 Khouribga, Morocco 123