MULTIPLE SOLUTIONS FOR A FRACTIONAL p-LAPLACIAN EQUATION WITH SIGN -CHANGING POTENTIAL

We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the fractional p-Laplace equation (-Delta)(p)(s)u broken vertical bar V(x)vertical bar u vertical bar(p-2)u = f (x, u) in R-N, where s is an element of(0, 1), p >= 2, N >= 2, (-Delta)(p)(s) is the fractional p -Laplace operator, the nonlinearity f is p-superlinear at infinity and the potential V(x) is allowed to be sign-hanging.