A Kirchhoff Type Equation in RN Involving the fractional (p, q)-Laplacian

In this paper, we deal with the following class of fractional (p, q)-Laplacian Kirchhoff type problem: {(1+[u]s,pp)(-Δ)psu+(1+[u]s,qq)(-Δ)qsu+V(εx)(|u|p-2u+|u|q-2u)=f(u)inRN,u∈Ws,p(RN)∩Ws,q(RN),u>0inRN,where ε> 0 , s∈ (0 , 1) , 1<2q, (-Δ)ts, with t∈ { p, q} , is the fractional t-Laplacian operator, V: RN→ R is a positive continuous potential such that inf ∂ΛV> inf ΛV for some bounded open set Λ ⊂ RN, and f: R→ R is a superlinear continuous nonlinearity with subcritical growth at infinity. By combining the method of Nehari manifold, a penalization technique, and the Lusternik–Schnirelman category theory, we study the multiplicity and concentration properties of solutions for the above problem when ε→ 0.