Existence of solutions for a class of obstacle problems with \(L^1\)-data and without sign condition (Q337965)

The authors prove the existence of at least one entropy solution to an anisotropic obstacle problem with variable exponent. The data are taken in \(L^1\) and the nonlinearity satisfies some growth condition related to the exponents of the operator, but no sign condition is assumed. The proof is based on the resolution of an approximated problem and the obtention of adequate estimates which allow the passage to the limit.