On solutions of nonlinear elliptic equations with $L_1$-data in $R^n$-space

Quasilinear elliptic equations of second order with summable right-hand side are considered in $R^n$-space. Restrictions on the structure of the equations are formulated in terms of a generalized $N$-function. The existence and uniqueness of entropic and renormalized solutions are proved in non-reflexive Muzilak-Orlich-Sobolev spaces. The equivalence of entropic and renormalized solutions of the considered equations in the $R^n$-space is established.