摘要：In the present paper, by using the variational and topological methods, we obtain a multiplicity and bifurcation result for the following fractional problems involving critical nonlinearities and a lower order perturbation: where Ω is an open and bounded domain with Lipschitz boundary, $N>2s$, with $s\in (0,1)$, g is a lower order perturbation of the critical power $ v ^{2_{s}^{*}-2}v$ and μ is a positive real parameter, $2_{s}^{*}=\frac{2N}{N-2s}$ is the fractional critical Sobolev exponent, while $\mathcal{L}_{K}$ is an integro-differential operator. Precisely, we show that the number of nontrivial solutions for this equation under suitable assumptions is at least twice the multiplicity of the eigenvalue. Our conclusions improve the related results in some respects.
