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A. M. A. Ahmed, The iterative technique for a fourth-order three-point nonlinear BVP with changing sign Green’s function, Eur. J. Math. Appl. 5 (2025), Article ID 16.

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Volume 5 (2025), Article ID 16

https://doi.org/10.28919/ejma.2025.5.16

Published: 21/10/2025

Abstract:

In this paper, we discuss the existence of a monotonic positive solution for the following fourth-order three points.
Non-linear BVP:
\begin{equation*}
\left\{\begin{array}{ll}u^{(4)}(t)=\lambda f (t,u(t)) ,\quad t \in [0,1],\\ u^{\prime}(0)=u^{\prime\prime\prime}(0)= u(1)=0,\\ \alpha u(0)+u^{\prime\prime}(\eta)=0 \end{array}\right.
\end{equation*}
which has the sign-changing Green’s function, where$\alpha\in[0,2)$,$f \in C([0,1]\times[0,+\infty),[0,+\infty))$ and $\eta\in[\frac{1}{2},1)$. The point is that although the corresponding Green is changing the sign, by applying iterative methods, We can still obtain the existence of a monotonic positive solution under certain suitable conditions of $f$.

How to Cite:

A. M. A. Ahmed, The iterative technique for a fourth-order three-point nonlinear BVP with changing sign Green’s function, Eur. J. Math. Appl. 5 (2025), Article ID 16. https://doi.org/10.28919/ejma.2025.5.16