Equivalence of Entropy and Renormalized Solutions of Nonlinear Elliptic Equations with \(L_{1}\)-Data in the Space \(\mathbb{R}^{n}\)

The paper considers elliptic equations of the second order with nonlinearities determined by the Musielak–Orlicz functions and the summable right-hand side. In non-reflexive Musielak–Orlicz–Sobolev spaces, the equivalence of entropy and renormalized solutions in the space \(\mathbb{R}^{n}\) is proved and their existence and uniqueness are established.