RN上分数阶Schrodinger方程的基态解

In this paper, we study a kind of time-independent fractionalSchr"odinger equation. By variational method, we prove the existence of ground state solutions when the potential $V(x)$ is unbounded and the nonlinearity $g(x)$ is subcritical and satisfies only the following geometry condition egin{eqnarray*}limsuplimits_{t ightarrow0^+} rac{2int_0^{t}g( au)d au}{t^2}<infsigma((-Delta)^{s}+V(x))<liminflimits_{t ightarrow+infty} rac{2int_0^{t}g( au)d au}{t^2}. end{eqnarray*}