论文标题
一类1-D超线性不确定问题的阳性解决方案的全局分叉图
Global bifurcation diagrams of positive solutions for a class of 1-D superlinear 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BVP的阳性解决方案的结构。这是数学分析如何有助于问题的数值研究的范式，而其数值研究也证实并阐明了分析。在分析方面，我们将积极解决方案的快速衰变确定为$λ\ downarrow -\ infty $，在该地区，$ a（x）<0 $（请参阅（1.1）），以及模型的抛物面对应物的解决方案（请参阅（1.2））为$λ\λ\λ\ downarrow- \ infty $ 0 $ 0 $ 0 $ 0 $ 0 $ 0. 0 $ 0 $ [提供$ u_0 $是（1.1）的订阅。该结果为我们提供了[28]在动态性质的附加条件下的猜想的证明。在数字方面，本文确定了某些范式原型的一组正溶液的全局结构，这些原型的复杂行为与现有的分析结果相去甚远。
This paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp's. It is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously its numerical study confirms and illuminates the analysis. On the analytical side, we establish the fast decay of the positive solutions as $λ\downarrow -\infty$ in the region where $a(x)<0$ (see (1.1)), as well as the decay of the solutions of the parabolic counterpart of the model (see (1.2)) as $λ\downarrow-\infty$ on any subinterval of $[0,1]$ where $u_0=0$, provided $u_0$ is a subsolution of (1.1). This result provides us with a proof of a conjecture of [28] under an additional condition of a dynamical nature. On the numerical side, this paper ascertains the global structure of the set of positive solutions on some paradigmatic prototypes whose intricate behavior is far from predictable from existing analytical results.
