TY - JOUR
T1 - Eigenvalues of Fourth-Order Singular Sturm-Liouville Boundary Value Problems
AU - Zhou , Lina
AU - Jiang , Weihua
AU - Li , Qiaoluan
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 485
EP - 493
PY - 2021
DA - 2021/04
SN - 2
DO - http://doi.org/10.12150/jnma.2020.485
UR - https://global-sci.org/intro/article_detail/jnma/18823.html
KW - Sturm-Liouville problems, Eigenvalue, Krasnoselskii's fixed-point
theorem.
AB - <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>