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arXiv · 2204.06244

Basisness and completeness of Fucik eigenfunctions for the Neumann Laplacian

Falko Baustian·Vladimir Bobkov
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Abstract

We investigate the basis properties of sequences of Fucik eigenfunctions of the one-dimensional Neumann Laplacian. We show that any such sequence is complete in $L^2(0,\pi)$ and a Riesz basis in the subspace of functions with zero mean. Moreover, we provide sufficient assumptions on Fucik eigenvalues which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in $L^2(0,\pi)$ and we explicitly describe the corresponding biorthogonal system.

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BibTeXRIS

Falko Baustian, Vladimir Bobkov. 2022-04-13. Basisness and completeness of Fucik eigenfunctions for the Neumann Laplacian. https://doi.org/10.1016/j.jmaa.2022.126466

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