Multiplicity of Solutions for Nonlocal Elliptic System of (p, q)‐Kirchhoff Type

This paper is concerned with the following nonlocal elliptic system of (p,q)-Kirchhofftype −[M1(∫Ω|∇u|p)]p−1Δpu=λFu(x,u,v), in Ω, −[M2(∫Ω|∇v|q)]q−1Δqv=λFv(x,u,v), in Ω, u=v=0, on ∂Ω. Under bounded condition on M and some novel and periodic condition on F, some newresults of the existence of two solutions and three solutions of the above mentioned nonlocal elliptic system are obtained bymeans of Bonanno's multiple critical points theorems without the Palais-Smale conditionand Ricceri's three critical points theorem, respectively