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$L^{\ell}-$Asymptotic properties of nonlinear Sturm-Liouville problems | ||
| Computational Methods for Differential Equations | ||
| مقاله 18، دوره 14، شماره 2، تیر 2026، صفحه 766-779 اصل مقاله (412.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.64894.2957 | ||
| نویسندگان | ||
| Fatemeh Kiyaee؛ Seyfollah Mosazadeh* | ||
| Department of Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran. | ||
| چکیده | ||
| In this paper, a nonlinear eigenvalue problem consisting of a nonlinear Sturm-Liouville equation $-y''- q(x)y= \lambda q^{-1}(x) y^{r}$ with Dirichlet boundary conditions on the interval $(-1/2 , 1/2)$ is investigated, where $\lambda >0$ is the eigenparameter. We provide a simple scheme to obtain the asymptotic behavior of $L^{\ell}-$bifurcation curve $\lambda=\lambda_{\ell}(\gamma)$ as $\gamma\longrightarrow 0$, where $\gamma=|| y_{\lambda}||_{\ell}$, $\ell \geq 1$, and $y_{\lambda}$ is the solution of Dirichlet problem associated with $\lambda$. | ||
| کلیدواژهها | ||
| Nonlinear Sturm-Liouville problem؛ $L^{\ell}-bifurcation curve؛ Asymptotic behavior؛ Eigenvalue | ||
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آمار تعداد مشاهده مقاله: 157 تعداد دریافت فایل اصل مقاله: 147 |
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