Complete structure of the Fucik spectrum of the p-Laplacian with integrable potentials on an interval

Wei Chen Department of Mathematics, College of Science, Hohai University Jifeng Chu Department of Mathematics, College of Science, Hohai University Ping Yan Department of Mathematical Sciences, Tsinghua University Meirong Zhang Department of Mathematical Sciences, Tsinghua University

Classical Analysis and ODEs mathscidoc:1611.05002

Communications in Contemporary Mathematics, 18, (6), 1550085, 2016
To characterize the complete structure of the Fucik spectrum of the p-Laplacian on higher dimensional domains is a long-standing problem. In this paper, we study the p-Laplacian with integrable potentials on an interval under the Dirichlet or the Neumann boundary conditions. Based on the strong continuity and continuous differentiability of solutions in potentials, we will give a comprehensive characterization of the corresponding Fucik spectra: each of them is composed of two trivial lines and a double-sequence of differentiable, strictly decreasing, hyperbolic-like curves; all asymptotic lines of these spectral curves are precisely described by using eigenvalues of the p-Laplacian with potentials; and moreover, all these spectral curves have strong continuity in potentials, i.e. as potentials vary in the weak topology, these spectral curves are continuously dependent on potentials in a certain sense.
p-Laplacian, integrable potentials, Fucik spectrum, asymptotic lines, strong continuity
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@inproceedings{wei2016complete,
  title={Complete structure of the Fucik spectrum of the p-Laplacian with integrable potentials on an interval},
  author={Wei Chen, Jifeng Chu, Ping Yan, and Meirong Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161124105127361810635},
  booktitle={Communications in Contemporary Mathematics},
  volume={18},
  number={6},
  pages={1550085},
  year={2016},
}
Wei Chen, Jifeng Chu, Ping Yan, and Meirong Zhang. Complete structure of the Fucik spectrum of the p-Laplacian with integrable potentials on an interval. 2016. Vol. 18. In Communications in Contemporary Mathematics. pp.1550085. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161124105127361810635.
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