Ground states for a class of generalized fractional Kirchhoff-type problem

In this paper, we investigate the fractional Kirchhoff-type equation $$ M \Big ( {\int\int_{\mathbb{R}^3\times \mathbb{R}^3}} \frac{|u(x)-u(y)|^2} {|x-y|^{3+2s}}dxdy \Big ) (-\Delta )^su(x)+V(x) u=f(x,u), $$ where \(M(t)\) is a continuous function, $(-\Delta)^s$ denotes the fractional Laplacian with \(s \in \left(\frac{3}{4}, 1\right)\), and both \(V\) and \(f\) exhibit asymptotic periodicity in \(x\). We establish the existence of a positive ground state solution, thereby extending and refining previous results by allowing more general Kirchhoff functions and asymptotically periodic nonlinearities.