Year: 2024
Author: Xingfang Feng, Hanying Feng
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 56–70
Abstract
In this paper, the existence of positive solutions of the following third-order three-point boundary value problem with $p$-Laplacian $$\begin{cases}(\phi_p(u''(t)))'+f(t,u(t))=0, \ t\in(0,1), \\ u(0)=\alpha u(\eta),\ u(1)=\alpha u(\eta), \ u''(0)=0, \end{cases}$$is studied, where $\phi_p(s) = |s|^{p−2} s,$ $p > 1.$ 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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.56
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 56–70
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Positive solution three-point boundary value problem fixed point index $p$-Laplacian operator.