In this work, we study the following nonlinear homogeneous Neumann boundary value problem $β(u)−diva(x,∇u) ∋ f in Ω, a(x,∇u)⋅η$ $=0$ on $∂Ω$, where $Ω$ is a smooth bounded open domain in $ℜ^N, N ≥ 3$ with smooth boundary $∂Ω$ and $η$ the outer unit normal vector on $∂Ω$. We prove the existence and uniqueness of an entropy solution for L¹-data f. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.
}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v27.n1.1}, url = {https://global-sci.com/article/88290/emlemsup1sup-existence-and-uniqueness-of-entropy-solutions-to-nonlinear-multivalued-elliptic-equations-with-homogeneous-neumann-boundary-condition-and-variable-exponent} }