LAUSR

Abstract In this paper we deal with the following fractional p&q-Laplacian problem: { ( − Δ ) p s u + ( − Δ ) q s u + V ( e x ) ( | u | p − 2 u + | u | q − 2 u ) = f ( u )  in  R N , u ∈ W s , p ( R N ) ∩ W s , q ( R N ) , u > 0  in  R N , where s ∈ ( 0 , 1 ) , e > 0 is a small parameter, 2 ≤ p q N s , ( − Δ ) t s , with t ∈ { p , q } , is the fractional ( s , t ) -Laplacian operator, V : R N → R is a continuous function satisfying the global Rabinowitz condition, and f : R → R is a continuous function with subcritical growth. Using suitable variational arguments and Ljusternik-Schnirelmann category theory, we prove that the above problem admits multiple solutions for e > 0 small enough.