论文标题
加权无限问题的节点解决方案
Nodal solutions of weighted indefinite problems
论文作者
论文摘要
本文分析了一类一维超值不确定的边界边界值问题的结构，并在光谱参数前面具有不确定的重量功能。令人惊讶的是，相关的高级特征值可能不会凹入，因为它是最低的。结果，在许多情况下，节点溶液可以从微不足道的溶液中分为三个甚至四个分叉点。本文结合了分析和数值工具。进行的分析是数学分析如何有助于问题的数值研究的一个范式，而同时的数值研究确认并阐明了分析。
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the associated high order eigenvalues might not be concave as it is the lowest one. As a consequence, in many circumstances the nodal solutions can bifurcate from three or even four bifurcation points from the trivial solution. This paper combines analytical and numerical tools. The analysis carried over on it is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously the numerical study confirms and illuminate the analysis.
