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We prove the existence of entropy solutions to unilateral problems associated to equations of the type $Au-div\left(\varphi \left(u\right)\right)=\mu \in L¹\left(\Omega \right)+W^{-1,p^{\text{'}}\left(·\right)}\left(\Omega \right)$, where A is a Leray-Lions operator acting from $W{₀}^{1,p\left(·\right)}\left(\Omega \right)$ into its dual $W^{-1,p\left(·\right)}\left(\Omega \right)$ and $\varphi \in C⁰(ℝ,{ℝ}^N)$.