Existence of least energy sign-changing solution for a class of fractional p&q-Laplacian problems with potentials vanishing at infinity

Abstract

In this paper, we consider the fractional p &q -Laplacian equation: ( − Δ ) p s u + ( − Δ ) q s u + V ( x ) ( | u | p − 2 u + | u | q − 2 u ) = K ( x ) f ( u ) in R N , where s ∈ ( 0 , 1 ) , 1 < p < q < N s , and ( − Δ ) t s with t ∈ { p , q } is the fractional t-Laplacian operator, f is a C 1 real function and V, K are continuous, positive functions. By using constrained variational methods, a quantitative Deformation Lemma and Brouwer degree theory, we prove the existence of a least energy sign-changing solution.