Rabinowitz无界连续体的一般性质

IF 2.1 2区数学 Q1 MATHEMATICS

Advanced Nonlinear Studies Pub Date : 2022-07-16 DOI:10.1515/ans-2022-0062

D. Bartolucci, Yeyao Hu, Aleks Jevnikar, Wen Yang

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引用次数: 1

摘要

摘要本文证明了在广义变分意义下，非线性特征值问题的任意解要么是非退化的，要么满足Crandall-Rabinowitz横截性条件。然后我们推断，一般地，解的无界Rabinowitz连续统是一个简单的解析曲线。全局分岔图类似于二维的Gel 'fand问题的经典模型。

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Generic properties of the Rabinowitz unbounded continuum

Abstract In this article, we prove that, generically in the sense of domain variations, any solution to a nonlinear eigenvalue problem is either nondegenerate or the Crandall-Rabinowitz transversality condition that is satisfied. We then deduce that, generically, the unbounded Rabinowitz continuum of solutions is a simple analytic curve. The global bifurcation diagram resembles the classic model case of the Gel’fand problem in two dimensions.

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来源期刊

Advanced Nonlinear Studies 数学-数学

CiteScore

3.00

自引率

5.60%

发文量

审稿时长

12 months

期刊介绍： Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.