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GROUND STATES FOR FRACTIONAL SCHR?DINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL GROWTH

更新时间:2023-05-28

【摘要】In this article, we study the following fractional Schr?dinger equation with electromagnetic fields and critical growth (-?)Asu + V(x)u = |u|2s*-2 u + λf(x, |u|2)u, x ∈ RN,where(-?)As is the fractional magnetic operator with 0 2s, λ > 0, 2s*=2N/(N-2s),f is a continuous function, V ∈ C(RN, R) and A ∈ C(RN, RN) are the electric and magnetic potentials, respectively. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method.

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