Abstract

We study the following nonlinear fractional Choquard equation:

where $\epsilon >0$, $s\in \left(0,1\right)$, $N>2s$, $I_{\theta }$ is the Riesz potential with order $\theta \in \left(0,N\right)$, $p\in \left[2,\frac{N+\theta }{N-2s}\right)$, $\underset{{ℝ}^N}{min}V>0$ and $\underset{{ℝ}^N}{inf}W>0$. By specifying the ranges and interdependence of linear and nonlinear potentials, we achieve the existence, convergence, concentration, and decay estimate of positive groundstates for $\star$. 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.

Keywords

Mathematical Subject Classification 2010

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