@article{724558,
      recid = {724558},
      author = {Chen, Zhijie,},
      title = {Solutions of nonlinear Schrödinger systems [electronic  resource] /},
      pages = {1 online resource.},
      abstract = {The existence and qualitative properties of nontrivial  solutions for some important nonlinear Schrℓʹdinger systems  have been studied in this thesis. For a well-known system  arising from nonlinear optics and Bose-Einstein condensates  (BEC), in the subcritical case, qualitative properties of  ground state solutions, including an optimal parameter  range for the existence, the uniqueness and asymptotic  behaviors, have been investigated and the results could  firstly partially answer open questions raised by  Ambrosetti, Colorado and Sirakov. In the critical case, a  systematical research on ground state solutions, including  the existence, the nonexistence, the uniqueness and the  phase separation phenomena of the limit profile has been  presented, which seems to be the first contribution for BEC  in the critical case. Furthermore, some quite different  phenomena were also studied in a more general critical  system. For the classical Brezis-Nirenberg critical  exponent problem, the sharp energy estimate of least energy  solutions in a ball has been investigated in this study.  Finally, for Ambrosetti type linearly coupled Schrℓʹdinger  equations with critical exponent, an optimal result on the  existence and nonexistence of ground state solutions for  different coupling constants was also obtained in this  thesis. These results have many applications in Physics and  PDEs.},
      url = {http://library.usi.edu/record/724558},
      doi = {https://doi.org/10.1007/978-3-662-45478-7},
}