Title: Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials,
Abstract: This paper is concerned with the following fractional Schrödinger
equations 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 the
fractional Laplacian operator with $\alpha\in(0,1)$, $N\geq2$, $\lambda$ is a
positive real parameter and $2_{\alpha}^{*}=2N/(N-2\alpha)$ is the critical
Sobolev exponent, $V(x)$ and $k(x)$ are positive and bounded functions
satisfying some extra hypotheses. Based on the principle of concentration
compactness in the fractional Sobolev space and the minimax arguments, we
obtain the existence of a nontrivial radially symmetric weak solution for the
above-mentioned equations without assuming the Ambrosetti-Rabinowitz condition
on the subcritical nonlinearity.