In this paper, we mainly study the fractional elliptic equation: (a+bₑ^₃| (-) ^s{2}u|^2dx) (-) ^su+u= (|x|^-*|u|^p) |u|^p-2u, x^3, where (0, 3), s (0, 1), 2-30. For this equation, we will discuss it in two case. For s (0, 34], we prove the existence of solutions by establishing an equivalent system. For s (34, 1), we use the symmetric mountain pass lemma to prove that the equation has infinitely many solutions.
Guo et al. (Mon,) studied this question.
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