In this article, we consider the following anisotropic nonlocal Schrödinger type equation Formula: see text in two different cases allowing the potential Formula: see text to be bounded and unbounded, where Formula: see text is known as anisotropic Formula: see text-Laplacian, Formula: see text, and Formula: see text is a parameter. The nonlinearity Formula: see text is a continuous function that behaves like Formula: see text as Formula: see text, and Formula: see text is the primitive of Formula: see text. By establishing the Hardy–Littlewood–Sobolev inequality in anisotropic setting and employing the anisotropic Trudinger–Moser inequality, we prove the existence of mountain–pass type positive weak solutions.
DAS et al. (Fri,) studied this question.