Resumen de Multiplicity and concentration of nontrivial nonnegative solutions for a fractional Choquard equation with critical exponent

Shaoxiong Chen, Yue Li, Zhipeng Yang

• In present paper, we study the fractional Choquard equation ε2s (−)s u + V(x)u = εμ−N 1 |x| μ ∗ F(u) f (u) + |u| 2∗ s −2u where ε > 0 is a parameter, s ∈ (0, 1), N > 2s, 2∗ s = 2N N−2s and 0 <μ< min{2s, N − 2s}.

  Under suitable assumption on V and f , we prove this problem has a nontrivial nonnegative ground state solution. Moreover, we relate the number of nontrivial nonnegative solutions with the topology of the set where the potential attains its minimum values and their’s concentration behavior