Pseudoindex theory and Nehari method for a fractional Choquard equation

We study the following nonlinear fractional Choquard equation: (*) epsilon(2s)(-Delta)(s)w + V(x)w = epsilon(-theta)w(x)[I-theta * (W vertical bar w vertical bar(p-2)w,( )x( )is an element of R- (N), where epsilon > 0, s is an element of (0, 1), N > 2s, I a is the Riesz potential with order theta is an element of (0, N), p is an element of [2, N+theta/N-2s), miu R-N V > 0 and inf(R)N W > 0. By specifying the ranges and interdependence of linear and nonlinear potentials, we achieve the existence, convergence, concentration, and decay estimate of positive ground-states for (*). The multiplicity of semiclassical solutions is established via pseudoindex theory. The existence of sign-changing solutions is constructed by minimizing the energy on Nehari nodal set.