【摘 要】
：
In a joint work with D. Bonheure and M. Nys, we have proved that groundstates of the magnetic nonlinear Schr(o)dinger equation -(▽-iA)2u + u = |u|p-2u in R
【机 构】
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CatholicalUniversitydeLouvain,Belgium
【出 处】
：
2016年非线性偏微分方程和变分方法及其应用研讨会(Workshop on Nonlinear PDEs and Cal
论文部分内容阅读
In a joint work with D. Bonheure and M. Nys, we have proved that groundstates of the magnetic nonlinear Schr(o)dinger equation -(▽-iA)2u + u = |u|p-2u in RN, inherit the symmetries of the magnetic field curlA when the latter is constant and small, allowing to obtain informations on the decay and on the asymptotics of the groundstate level. In collaboration with D. Ruiz, we have showed that the least action odd solutions to the general Choquard equation -△u + u =(Iα*|u|p)|u|p-2u in RN have an odd symmetry with respect to a reflection when the order α of the Riesz potential is either close to 0 or close to N. I will explain how we have managed to exploit the nondegeneracy of the nonlinear Schr(o)dinger equation, which is the natural limiting problem, in situations in which the problems lie in different functional spaces or the solutions behave asymptotically as two bumps spreading apart. This is joint work with D. Bonheure (Bruxelles) and M. Nys (Torino), and with D. Ruiz (Granada).
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