Schrödinger–Kirchhoff–Hardy $ p $–fractional equations without the Ambrosetti–Rabinowitz condition

This paper is devoted to the study of the following Schrödinger–Kirchhoff–Hardy equation in $ \mathbb R^n $

$ M\left(\iint_{\mathbb R^{2n}}\frac{|u(x)-u(y)|^p}{|x-y|^{n+ps}}dxdy\right)(-\Delta)^{s}_pu+V(x)|u|^{p-2}u-\mu\frac{|u|^{p-2}u}{|x|^{ps}} = f(x, u), $

where $ (-\Delta)^s_p $ is the fractional $ p $–Laplacian, with $ s\in(0, 1) $ and $ p>1 $, dimension $ n>ps $, $ M $ models a Kirchhoff coefficient, $ V $ is a positive potential, $ f $ is a continuous nonlinearity and $ \mu $ is a real parameter. The main feature of the paper is the combination of a Kirchhoff coefficient and a Hardy term with a suitable function $ f $ which does not necessarily satisfy the Ambrosetti–Rabinowitz condition. Under different assumptions for $ f $ and restrictions for $ \mu $, we provide existence and multiplicity results by variational methods.