TY - JOUR
T1 - Positive Solutions for Third Order Three-Point Boundary Value Problems with $p$-Laplacian
AU - Feng , Xingfang
AU - Feng , Hanying
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 56
EP - 70
PY - 2024
DA - 2024/03
SN - 6
DO - http://doi.org/10.12150/jnma.2024.56
UR - https://global-sci.org/intro/article_detail/jnma/22966.html
KW - Positive solution, three-point boundary value problem, fixed point
index, $p$-Laplacian operator.
AB - <p style="text-align: justify;">In this paper, the existence of positive solutions of the following
third-order three-point boundary value problem with $p$-Laplacian $$\begin{cases}(\phi_p(u&#39;&#39;(t)))&#39;+f(t,u(t))=0, \ t\in(0,1), \\ u(0)=\alpha u(\eta),\ u(1)=\alpha u(\eta), \ u&#39;&#39;(0)=0,&nbsp; \end{cases}$$is studied, where $\phi_p(s) = |s|^{p−2} s,$ $p &gt; 1.$ By using the fixed point index
method, we establish sufficient conditions for the existence of at least one or
at least two positive solutions for the above boundary value problem. The
main result is demonstrated by providing an example as an application.</p>