论文标题
Fuč\'ık光谱的第一曲线的变分特性用于椭圆操作员
Variational properties of the first curve of the Fuč\'ık spectrum for elliptic operators
论文作者
论文摘要
在本文中，我们介绍了Fuč\'ıkSpectrum的第一条非数字曲线的新变化特征，该曲线对于具有Dirichlet边界条件的椭圆算子。此外，我们描述了该曲线的渐近行为和某些特性和相应的本征函数。特别是，这种新的特征使我们能够将fuč\'ık频谱的第一条曲线与以前的作品中获得的无限多曲线进行比较（请参阅R. Molle，D。Passaseo，Fuč\'ıkSpectrum。C.R.R.Math。Acad。Sci。Sci。Sci。Sci。Sci。Paris351（2013），No。17/18，6818，6818，6818,68,68,68,68,68,68,68,68,6818 185,68,68,68,68,68,68,68,68,68,68,68,68,68,68,68,6818,68,68，R. fuč\'s spectrum的许多新曲线。
In this paper we present a new variational characteriztion of the first nontrival curve of the Fuč\'ık spectrum for elliptic operators with Dirichlet boundary conditions. Moreover, we describe the asymptotic behaviour and some properties of this curve and of the corresponding eigenfunctions. In particular, this new characterization allows us to compare the first curve of the Fuč\'ık spectrum with the infinitely many curves we obtained in previous works (see R. Molle, D. Passaseo, New properties of the Fuč\'ık spectrum. C. R. Math. Acad. Sci. Paris 351 (2013), no. 17/18, 681--685 and R. Molle, D. Passaseo, Infinitely many new curves of the Fuč\'ık spectrum. Ann. I. H. Poincaré - AN (2014), http://dx.doi.org/10.1016/j.anihpc.2014.05.007): for example, we show that these curves are all asymptotic to the same lines as the first curve, but they are all distinct from such a curve.
