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

In this paper, 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.