University of Tabriz Computational Methods for Differential Equations 2345-3982 14 2 2026 04 01 $L^{\ell}-$Asymptotic properties of nonlinear Sturm-Liouville problems 766 779 19718 10.22034/cmde.2025.64894.2957 EN Fatemeh Kiyaee Department of Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran. Seyfollah Mosazadeh Department of Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran. Journal Article 2024 12 06 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 $\lambda$. https://cmde.tabrizu.ac.ir/article_19718_9cf090a0529b5a173416546ba892bbb1.pdf