Infinitely many radial and non-radial solutions for a fractional Schrödinger equation

In this paper, we study the following fractional Schrodinger equation ( - Δ ) s u + V ( | x | ) u = f ( | x | , u ) , x ? R N , where ( - Δ ) s ( s ? ( 0 , 1 ) ) denotes the fractional Laplacian. By variational methods, we obtain the existence of a sequence of radial solutions for N ? 2 , a sequence of non-radial solutions for N = 4 or N ? 6 , and a non-radial solution for N = 5 .

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