EXISTENCE OF INFINITELY MANY SOLUTIONS FOR FRACTIONAL p-LAPLACIAN EQUATIONS WITH SIGN-CHANGING POTENTIAL

In his article, we prove the existence of infinitely many solutions for the fractional p-Laplacian equation (-Delta)(p)(s)u+ v(x)|u|(p-2)u = f (x, u), x is an element of R-N where s is an element of (0, 1), 2 <= p < infinity. Based on a direct sum decomposition of a space E-S, we investigate the multiplicity of solutions for the fractional p-Laplacian equation in R-N. The potential V is allowed to be sign-changing, and the primitive of the nonlinearity f is of super-p growth near infinity in u and allowed to be sign-changing. Our assumptions are suitable and different from those studied previously.