Non--Coercive Elliptic Problems with Measure Data in Musielak--Orlicz Spaces

Abstract

In this research, we investigate a class of nonlinear elliptic equations with measure data in Musielak--Orlicz spaces, under non-coercive growth conditions. Using the framework of renormalized solutions, we establish existence results by combining modular estimates and truncation techniques. No \( \Delta_2 \)-condition is assumed on the Musielak function, and the datum is assumed to belong to \( L^1(\Omega) + W^{-1} E_{\overline{\varphi}}(\Omega) \). This work extends previous results to operators with nonstandard growth without coercivity.