On the Critical Kirchhoff Problems with Super-linear Nonlinearities and Variable Potentials

In this paper, we consider the following critical Kirchhoff equation. where μ is a positive parameter, a, b 0 are real constants, f ∈ C(R,R) and V ∈ C1(R3,R). Under some suitable conditions, the existence of ground state solution to the above problem is established without the monotonicity condition on f (u)/u3.Moreover, it is worth noting that we consider the above problem with variable potentials.Our results improve and extend related ones in the existing literature to some extent.