@Article{JNMA-2-4,
author = {Zhou, Lina and Weihua, Jiang and Qiaoluan, Li},
title = {Eigenvalues of Fourth-Order Singular Sturm-Liouville Boundary Value Problems},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2020},
volume = {2},
number = {4},
pages = {485--493},
abstract = {<p style="text-align: justify;">In this paper, by using Krasnoselskii&#39;s fixed-point theorem, some sufficient conditions of existence of positive solutions for the following fourth-order nonlinear Sturm-Liouville eigenvalue problem:\begin{equation*}\left\{\begin{array}{lll} \frac{1}{p(t)}(p(t)u&#39;&#39;&#39;)&#39;(t)+ \lambda f(t,u)=0, t\in(0,1), \\ u(0)=u(1)=0, \\ \alpha u&#39;&#39;(0)- \beta \lim_{t \rightarrow 0^{+}} p(t)u&#39;&#39;&#39;(t)=0, \\ \gamma u&#39;&#39;(1)+\delta\lim_{t \rightarrow 1^{-}} p(t)u&#39;&#39;&#39;(t)=0, \end{array}\right.\end{equation*} are established, where $\alpha,\beta,\gamma,\delta \geq 0,$ and $~\beta\gamma+\alpha\gamma+\alpha\delta &gt;0$. The function $p$ may be singular at $t=0$ or $1$, and $f$ satisfies Carathéodory condition.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2020.485},
url = {https://global-sci.com/article/88025/eigenvalues-of-fourth-order-singular-sturm-liouville-boundary-value-problems}
}