Existence Of Solutions For A Class Of Fractional P-Kirchhoff Systems

In this paper, we study the following non-homogeneous fractional p-Kirchhoff system where L_p³ is a non-local fractional operator with 0<s<1<p< +? such that ps < N, 1 < q < p,? is a bounded domain in RN with smooth boundary.Mi?i =1,2? are continuous functions, ? and ? are real parameters. a?x?,b?x? ?L^????with ?=p_s^*/p_s^*-q?p_s^*=Np/N-ps?, h₁?x?,h₂?x? ?L^v??? with v= ps*/ps*-1.Fu?x,u,v? and Fv?x,u,v? are the gradients of F?x,u,v? ? C¹??×R²,R?.The above system considers the general term F?x, u, v?, which makes the system more complex and more general. Under some suitable conditions, by making use of mountain pass theorem and Ekeland's variational principle, we obtain a positive energy solution and a negative energy solution of the above mentioned system.