By Zhijie Chen
The life and qualitative homes of nontrivial suggestions for a few vital nonlinear Schrӧdinger structures were studied during this thesis. For a widely known method coming up from nonlinear optics and Bose-Einstein condensates (BEC), within the subcritical case, qualitative homes of flooring kingdom strategies, together with an optimum parameter diversity for the lifestyles, the individuality and asymptotic behaviors, were investigated and the implications may to start with partly resolution open questions raised by means of Ambrosetti, Colorado and Sirakov. within the severe case, a systematical examine on floor country ideas, together with the life, the nonexistence, the individuality and the section separation phenomena of the restrict profile has been provided, which seems the 1st contribution for BEC within the serious case. in addition, a few relatively diverse phenomena have been additionally studied in a extra normal serious process. For the classical Brezis-Nirenberg severe exponent challenge, the pointy power estimate of least power suggestions in a ball has been investigated during this learn. ultimately, for Ambrosetti sort linearly coupled Schrӧdinger equations with serious exponent, an optimum consequence at the life and nonexistence of flooring kingdom ideas for various coupling constants used to be additionally received during this thesis. those effects have many purposes in Physics and PDEs.
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Solutions of Nonlinear Schrӧdinger Systems (Springer Theses) by Zhijie Chen
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