Existence and uniqueness for singular logarithmic double phase problems

Abstract In this work we study singular elliptic equations driven by the logarithmic double phase operator. We first establish the existence of at least one positive bounded weak solution under general structural conditions. Subsequently, we refine this result by proving uniqueness of a positive solution for a class of problems involving mild singularities at the origin and perturbed by sublinear growth nonlinearities. Our approach relies on the framework of pseudomonotone operators along with a new weak maximum principle specifically developed for the logarithmic double phase setting, which plays a key role in our analysis. To the best of our knowledge, this is the first contribution dealing with logarithmic double phase problems that include singular terms.