Positive solutions for a nonlocal Schrodinger type equation involving modified anisotropic N-Laplacian

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.