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This paper is concerned with the following fractional Schr\"{o}dingerequations involving critical exponents: \begin{eqnarray*}(-\Delta)^{\alpha}u+V(x)u=k(x)f(u)+\lambda|u|^{2_{\alpha}^{*}-2}u\quad\quad\mbox{in}\ \mathbb{R}^{N}, \end{eqnarray*} where $(-\Delta)^{\alpha}$ is thefractional Laplacian operator with $\alpha\in(0,1)$, $N\geq2$, $\lambda$ is apositive real parameter and $2_{\alpha}^{*}=2N/(N-2\alpha)$ is the criticalSobolev exponent, $V(x)$ and $k(x)$ are positive and bounded functionssatisfying some extra hypotheses. Based on the principle of concentrationcompactness in the fractional Sobolev space and the minimax arguments, weobtain the existence of a nontrivial radially symmetric weak solution for theabove-mentioned equations without assuming the Ambrosetti-Rabinowitz conditionon the subcritical nonlinearity.

Existence and symmetry of solutions for critical fractional Schr\"odinger equations with bounded potentials