Stationary even periodic solutions of the Swift-Hohenberg equation areanalyzed for the critical parameter k = 1, and it is proved that there exist periodic solutionshaving the same energy as the constant solution u = ...Stationary even periodic solutions of the Swift-Hohenberg equation areanalyzed for the critical parameter k = 1, and it is proved that there exist periodic solutionshaving the same energy as the constant solution u = 0. For k ≤ 0, some qualitative properties ofthe solutions are also proved.展开更多
This paper deals with the periodic solutions of Schrǒdinger flow from S^3 to S^2. It is shown that the periodic solution is related to the variation of some functional and there exist S^1-invariant critical points to...This paper deals with the periodic solutions of Schrǒdinger flow from S^3 to S^2. It is shown that the periodic solution is related to the variation of some functional and there exist S^1-invariant critical points to this functional. The proof makes use of the Principle of Symmetric Criticality of Palais.展开更多
文摘Stationary even periodic solutions of the Swift-Hohenberg equation areanalyzed for the critical parameter k = 1, and it is proved that there exist periodic solutionshaving the same energy as the constant solution u = 0. For k ≤ 0, some qualitative properties ofthe solutions are also proved.
基金Project supported by the National Natural Science Foundation of China (No.10321001).
文摘This paper deals with the periodic solutions of Schrǒdinger flow from S^3 to S^2. It is shown that the periodic solution is related to the variation of some functional and there exist S^1-invariant critical points to this functional. The proof makes use of the Principle of Symmetric Criticality of Palais.
