Abstract
Let \(\Omega \subset {\mathbb {R}}^{n}\) be a smooth bounded domain and \(m\in C(\overline{\Omega })\) be a sign-changing weight function. For \(1<p<\infty \), consider the eigenvalue problem
where \(\Delta _{p}u\) is the usual p-Laplacian. Our purpose in this article is to study the limit as \(p\rightarrow \infty \) for the eigenvalues \(\lambda _{k,p}\left( m\right) \) of the aforementioned problem. In addition, we describe the limit of some normalized associated eigenfunctions when \(k=1\).
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Acknowledgements
The research of UK was partially funded by Secyt-UNC 33620180100016CB (Argentina). The research of JDR was partially supported by CONICET grant PIP GI No 11220150100036CO (Argentina), by UBACyT grant 20020160100155BA (Argentina) and by MINECO MTM2015-70227-P (Spain). JT was partially supported by ANPCyT grant PICT 2016-1054 (Argentina) and by Secyt-UNC 33620180100016CB (Argentina).
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Kaufmann, U., Rossi, J.D. & Terra, J. The \(\infty \)-eigenvalue problem with a sign-changing weight. Nonlinear Differ. Equ. Appl. 26, 14 (2019). https://doi.org/10.1007/s00030-019-0561-y
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DOI: https://doi.org/10.1007/s00030-019-0561-y