论文标题
使用全局参数延续全局解决方案曲线
Continuation of global solution curves using global parameters
论文作者
论文摘要
本文通过延续全局参数提供了全局解决方案曲线的理论结果和数值计算。当全局参数变化时，将直接计算解决方案曲线上的每个点，以便解决方案曲线所产生的所有转弯以及其不同的分支都会自动出现在计算机屏幕上。对于径向$ p $ - 拉普拉斯方程，我们提出了从P. Korman [15]的正规化转换的简化推导，并使用此转换来进行更准确的数值计算。对于$ p> 2 $，解决方案不是$ c^2 $的类别，我们表明它们是$ w（r^{\ frac {p} {2（p-1）}}）$的形式，其中$ w（z）$属于$ c^2 $ class $ c^2 $。分叉图还针对非自主问题以及对弹性梁进行建模的第四阶方程计算。我们表明，解决方案的第一个谐波也可以用作全局参数。
This paper provides both the theoretical results and numerical calculations of global solution curves, by continuation in global parameters. Each point on the solution curves is computed directly as the global parameter is varied, so that all of the turns that the solution curves make, as well as its different branches, appear automatically on the computer screen. For radial $p$-Laplace equations we present a simplified derivation of the regularizing transformation from P. Korman [15], and use this transformation for more accurate numerical computations. While for $p>2$ the solutions are not of class $C^2$, we show that they are of the form $w(r^{\frac{p}{2(p-1)}})$, where $w(z)$ is of class $C^2$. Bifurcation diagrams are also calculated for non-autonomous problems, and for the fourth order equations modeling elastic beams. We show that the first harmonic of the solution can also serve as a global parameter.
