Neumann问题解的轨道分支
Bifurcations from the orbit of solutions of the Neumann problem
摘要：
研究了球上一类非线性Neumann问题的弱解。假设势是不变的，我们考虑临界点的轨道，即我们不假设临界点是孤立的。我们应用等变分析的技术来研究平凡解轨道的分叉。我们制定的充分条件的局部和整体的分歧，在右手边的系统和拉普拉斯算子的特征值。此外，我们还讨论了全局破缺现象发生的轨道。
英文摘要：
The purpose of this paper is to study weak solutions of a nonlinear Neumann problem considered on a ball. Assuming that the potential is invariant, we consider an orbit of critical points, i.e. we do not assume that critical points are isolated. We apply techniques of the equivariant analysis to examine bifurcations from the orbits of trivial solutions. We formulate sufficient conditions for local and global bifurcations, in terms of the right-hand side of the system and eigenvalues of the Laplace operator. Moreover, we characterise orbits at which the global symmetry-breaking phenomenon occurs.
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