$L^{\ell}-$Asymptotic properties of nonlinear Sturm-Liouville problems

Kiyaee, Fatemeh; Mosazadeh, Seyfollah

doi:10.22034/cmde.2025.64894.2957

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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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$L^{\ell}-$Asymptotic properties of nonlinear Sturm-Liouville problems