Energy dependent potential problems for the one dimensional p-Laplacian operator
In this work we analyze a nonlinear eigenvalue problem for the p-Laplacian operator with zero Dirichlet boundary conditions. We assume that the problem has a potential which depends on the eigenvalue parameter, and we show that, for n big enough, there exists a real eigenvalue λn, and their correspo...
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2019
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14681218_v45_n_p285_Koyunbakan http://hdl.handle.net/20.500.12110/paper_14681218_v45_n_p285_Koyunbakan |
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paper:paper_14681218_v45_n_p285_Koyunbakan2023-06-08T16:16:57Z Energy dependent potential problems for the one dimensional p-Laplacian operator Asymptotic behavior Eigenvalues Nodal inverse problem Asymptotic analysis Boundary conditions Inverse problems Laplace equation Laplace transforms Mathematical operators Asymptotic behaviors Asymptotic expansion Dirichlet boundary condition Eigenvalues Nonlinear eigenvalue problem One-dimensional p-Laplacian P-Laplacian operator Potential problems Eigenvalues and eigenfunctions In this work we analyze a nonlinear eigenvalue problem for the p-Laplacian operator with zero Dirichlet boundary conditions. We assume that the problem has a potential which depends on the eigenvalue parameter, and we show that, for n big enough, there exists a real eigenvalue λn, and their corresponding eigenfunctions have exactly n nodal domains. We characterize the asymptotic behavior of these eigenvalues, obtaining two terms in the asymptotic expansion of λn in powers of n. Finally, we study the inverse nodal problem in the case of energy dependent potentials, showing that some subset of the zeros of the corresponding eigenfunctions is enough to determine the main term of the potential. © 2018 Elsevier Ltd 2019 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14681218_v45_n_p285_Koyunbakan http://hdl.handle.net/20.500.12110/paper_14681218_v45_n_p285_Koyunbakan |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Asymptotic behavior Eigenvalues Nodal inverse problem Asymptotic analysis Boundary conditions Inverse problems Laplace equation Laplace transforms Mathematical operators Asymptotic behaviors Asymptotic expansion Dirichlet boundary condition Eigenvalues Nonlinear eigenvalue problem One-dimensional p-Laplacian P-Laplacian operator Potential problems Eigenvalues and eigenfunctions |
| spellingShingle |
Asymptotic behavior Eigenvalues Nodal inverse problem Asymptotic analysis Boundary conditions Inverse problems Laplace equation Laplace transforms Mathematical operators Asymptotic behaviors Asymptotic expansion Dirichlet boundary condition Eigenvalues Nonlinear eigenvalue problem One-dimensional p-Laplacian P-Laplacian operator Potential problems Eigenvalues and eigenfunctions Energy dependent potential problems for the one dimensional p-Laplacian operator |
| topic_facet |
Asymptotic behavior Eigenvalues Nodal inverse problem Asymptotic analysis Boundary conditions Inverse problems Laplace equation Laplace transforms Mathematical operators Asymptotic behaviors Asymptotic expansion Dirichlet boundary condition Eigenvalues Nonlinear eigenvalue problem One-dimensional p-Laplacian P-Laplacian operator Potential problems Eigenvalues and eigenfunctions |
| description |
In this work we analyze a nonlinear eigenvalue problem for the p-Laplacian operator with zero Dirichlet boundary conditions. We assume that the problem has a potential which depends on the eigenvalue parameter, and we show that, for n big enough, there exists a real eigenvalue λn, and their corresponding eigenfunctions have exactly n nodal domains. We characterize the asymptotic behavior of these eigenvalues, obtaining two terms in the asymptotic expansion of λn in powers of n. Finally, we study the inverse nodal problem in the case of energy dependent potentials, showing that some subset of the zeros of the corresponding eigenfunctions is enough to determine the main term of the potential. © 2018 Elsevier Ltd |
| title |
Energy dependent potential problems for the one dimensional p-Laplacian operator |
| title_short |
Energy dependent potential problems for the one dimensional p-Laplacian operator |
| title_full |
Energy dependent potential problems for the one dimensional p-Laplacian operator |
| title_fullStr |
Energy dependent potential problems for the one dimensional p-Laplacian operator |
| title_full_unstemmed |
Energy dependent potential problems for the one dimensional p-Laplacian operator |
| title_sort |
energy dependent potential problems for the one dimensional p-laplacian operator |
| publishDate |
2019 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14681218_v45_n_p285_Koyunbakan http://hdl.handle.net/20.500.12110/paper_14681218_v45_n_p285_Koyunbakan |
| _version_ |
1768545111295131648 |