Nonlinear weighted elliptic problem with variable exponents and \(L^1\) data

In this paper, we prove the existence of weak solutions for a class of nonlinear weighted elliptic equations in \(\Omega \) $\mathrm{\Omega }$ with p(x) growth conditions and integrable data. The functional setting involves Lebesgue-Sobolev spaces with variable exponents. Our results are generalizations of the corresponding results in the constant exponent case in L. Boccardo et al (Boll. Unione Mat. Ital. 15, No. 4, 503-514 (2022)) and some results given in D. Arcoya et al ( Journal of Functional Analysis, 268(5), 1153-1166 (2015)).