Fractional magnetic Schr{o}dinger equations with potential vanishing at infinity and supercritical exponents

This paper focuses on the following class of fractional magnetic Schr{o}dinger equations begin{equation*} (-Delta)_{A}^{s}u+V(x)u=g(vert uvert^{2})u+lambdavert uvert^{q-2}u, quad mbox{in } mathbb{R}^{N}, end{equation*} where $(-Delta)_{A}^{s}$ is the fractional magnetic Laplacian, $A :mathbb{R}^N rightarrow mathbb{R}^N$ is the magnetic potential, $sin (0,1)$, $N>2s$, $lambda geq0$ is a parameter, $V:mathbb{R}^N rightarrow mathbb{R}$ is a potential function that may decay to zero at infinity and $g: mathbb{R}_{+} rightarrow mathbb{R}$ is a continuous function with subcritical growth. We deal with supercritical case $qgeq 2^*_s:=2N/(N-2s)$. Our approach is based on variational methods combined with penalization technique and $L^{infty}$-estimates.