Bound state solutions of Choquard equations with a nonlocal operator

Abstract

In this paper, we study the following Choquard equation with Kirchhoff operator where a ≥ 0, b > 0, α ∈ (0, N), is the critical exponent respect to Hardy–Littlewood–Sobolev inequality, and is a given nonnegative function. By using the classical linking theorem and global compactness theorem, we prove that equation (0.1) has at least one bound state solution if is small. More intriguingly, our result covers a novel feature of Kirchhoff problems, which is the fact that the parameter a can be zero.