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| Properties around the First Eigenvalue of a Partial Discrete Dirichlet Boundary Value Problem |
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| KeyWord:Partial discrete Dirichlet problem, first eigenvalue, simplicity |
| Author Name | Affiliation | | Mohammed Abderrahim | University Mohamed I, Faculty of sciences, laboratory LaMAO, Oujda, Morocco | | Abdesslem Ayoujil | Regional Centre of Trades Education and Training Department of Mathematics Oujda, Morocco | | Mohammed Barghouthe | University Mohamed I, Faculty of sciences, laboratory LaMAO, Oujda, Morocco | | Mohammed Berrajaa | University Mohamed I, Faculty of sciences, laboratory LaMAO, Oujda, Morocco |
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| Abstract: |
| In this article, we study some results around the first eigenvalue $\lambda_{1, m}$ for the partial discrete Dirichlet boundary value problem, like the constant sign of the eigenfunction associated with $\lambda_{1, m}$, the simplicity of $\lambda_{1, m}$ and the sign change of any eigenfunction associated with $\lambda> \lambda_{1,m}$. |
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