Spectrum of Navier $p$-biharmonic problem with sign-changing weight

Guowei Dai

Spectrum of Navier $p$-biharmonic problem with sign-changing weight

Classical Analysis and ODEs 2016-08-30 v2

Authors: Guowei Dai

Abstract

In this paper, we consider the following eigenvalue problem {{l} (|u"|^{p-2}u")"=\lambda m(x)|u|^{p-2}u, x\in (0,1), u(0)=u(1)=u"(0)=u"(1)=0, where $1<p<+\infty$ , $\lambda$ is a real parameter and $m$ is sign-changing weight. We prove there exists a unique sequence of eigenvalues for above problem. Each eigenvalue is simple and continuous with respect to $p$ , the $k$ -th eigenfunction, corresponding to the $k$ -th positive or negative eigenvalue, has exactly $k-1$ generalized simple zeros in $(0,1)$ .

Keywords

Navier $p$-biharmonic problem eigenvalue problem sign-changing weight spectral theory generalized simple zeros nonlinear differential equations

Cite

@article{arxiv.1207.7159,
  title  = {Spectrum of Navier $p$-biharmonic problem with sign-changing weight},
  author = {Guowei Dai},
  journal= {arXiv preprint arXiv:1207.7159},
  year   = {2016}
}

Comments

The proof of Theorem 1.1 cotains a gap

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