Multiplicity of solutions for a scalar field equation involving a fractional p-Laplacian with general nonlinearity

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We prove the existence of infinitely many radially symmetric solutions to the problem ( − Δ p ) s u = g ( u ) in R N , u ∈ W s , p ( R N ) , where s ∈ ( 0 , 1 ) , 2 ≤ p < ∞ , sp ≤ N , 2 ≤ N ∈ N and ( − Δ p ) s is the fractional p-Laplacian operator. We treat both the cases sp = N and sp<N. The nonlinearity g is a function of Berestycki–Lions type with critical exponential growth if sp = N and critical polynomial growth if sp<N. We also prove the existence of a ground state solution for the same problem.