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

【摘要】 In this article, we study the following fractional Schr?dinger equation with electromagnetic fields and critical growth （-?）_A^su + V（x）u = |u|^2_s*-2 u + λf（x, |u|²）u, x ∈ R^N,where（-?）_A^s is the fractional magnetic operator with 0 < s < 1, N > 2s, λ > 0, 2_s^*=2N/（N-2s）,f is a continuous function, V ∈ C（R^N, R） and A ∈ C（R^N, R^N） 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.更多还原

【Abstract】 In this article, we study the following fractional Schr?dinger equation with electromagnetic fields and critical growth （-?）_A^su + V（x）u = |u|^2_s*-2 u + λf（x, |u|²）u, x ∈ R^N,where（-?）_A^s is the fractional magnetic operator with 0 < s < 1, N > 2s, λ > 0, 2_s^*=2N/（N-2s）,f is a continuous function, V ∈ C（R^N, R） and A ∈ C（R^N, R^N） 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.更多还原