Infinitely Many Solutions for the Fractional Nonlinear Schrodinger Equations of a New Type

This paper, we study the multiplicity of solutions for the fractional Schrodinger equation (-Delta)(s)u + V( x) u = u(p), u > 0, x is an element of R-N, u is an element of H-s(R-N), with s is an element of(0,1), N >= 3, p is an element of(1, 2N/N-2s -1) and lim(|y|->+infinity)V(y)> 0. By assuming suitable decay property of the radial potential V(y) = V(|y|), we construct another type of solutions concentrating at infinite vertices of two similar equilateral polygonal with infinitely large length of sides. Hence, besides the length of each polygonal, we must consider one more parameter, that is the height of the podetium, simultaneously. Another difficulty lies in the non-local property of the operator (-Delta)(s) and the algebraic decay involving the approximation solutions make the estimates become more subtle.