Existence and multiplicity of standing wave solutions for perturbed fractional p-Laplacian systems involving critical exponents

In this paper, we investigate the existence of standing wave solutions to the following perturbed fractional p-Laplacian systems with critical nonlinearity

$$\{\begin{array}{rl}& {\epsilon }^{ps}(-\mathrm{\Delta }{)}_p^{s}u+V(x)|u{|}^{p-2}u=K(x)|u{|}^{p_s^{\ast }-2}u+F_u(x,u,v),x\in {\mathbb{R}}^N,\\ & {\epsilon }^{ps}(-\mathrm{\Delta }{)}_p^{s}v+V(x)|v{|}^{p-2}v=K(x)|v{|}^{p_s^{\ast }-2}v+F_v(x,u,v),x\in {\mathbb{R}}^N.\end{array}$$

Under some proper conditions, we obtain the existence of standing wave solutions $(u_{\epsilon },v_{\epsilon })$ which tend to the trivial solutions as $\epsilon \to 0$. Moreover, we get $m$ pairs of solutions for the above system under some extra assumptions. Our results improve and supplement some existing relevant results.