Variable Supercritical Schrödinger-Poisson system with singular term

Abstract

In this paper, we consider a class of Schrödinger-Poisson systems on bounded domains that depend on a parameter η. These systems have variable supercritical exponents and a singular term as part of their nonlinearity. For η=1, we proved the existence and uniqueness of a solution using variational methods. In the case η=−1, the structure of the problem changes significantly, and we proved the existence of a solution using non-variational methods based on an approximating scheme. In both cases, we faced difficulties handling the loss of compactness because the variable exponents involve supercritical growth. The supercritical variable growth not only causes the system to lose its homogeneity but also its compactness properties.