一类带扰动的分数阶临界Choquard方程的正规解

Normalized solutions for a class of fractional critical Choquard equations with perturbation

研究一类分数阶Choquard方程的正规解,其中非线性项包含Hardy-Littlewood-Sobolev临界指数和带参数的质量超临界非局部项,分析Pohozaev流形的性质,建立了上述方程对应能量泛函的Palais-Smale序列的紧性条件。当扰动项的系数充分大时,获得了其正规基态解的存在性。

The normalized solutions for a class of fractional Choquard equations are studied,where Hardy-Littlewood-Sobolev critical exponent and mass supercritical nonlocal term with the parameter are contained in nonlinearites.By analyzing the properties of Pohozaev manifold,the compact condition of Palais-Smale sequences for the energy functional corresponding to above equations is established.When the coefficient of perturbation is large enough,the existence of normalized ground state solutions is obtained.