Department of Mathematics
IIT Patna, India
email: nazia.pma17@iitp.ac.in
Department of Mathematics
IIT Patna, India
email: akverma@iitp.ac.in
Nazia Urus, Amit K. Verma
Abstract:
In this article, we establish the existence of solutions for a
fourth-order four-point non-linear boundary value problem (BVP)
which arises in bridge design,
$$\displaylines{
- y^{(4)}( s)-\lambda y''( s)=\mathcal{F}( s, y( s)), \quad s\in(0,1),\cr
y(0)=0,\quad y(1)= \delta_1 y(\eta_1)+\delta_2 y(\eta_2),\cr
y''(0)=0,\quad y''(1)= \delta_1 y''(\eta_1)+\delta_2 y''(\eta_2),
}$$
where \(\mathcal{F} \in C([0,1]\times \mathbb{R},\mathbb{R})\), \(\delta_1, \delta_2>0\),
\(0<\eta_1\le \eta_2 <1\), \(\lambda=\zeta_1+\zeta_2 \), where
\(\zeta_1\) and \(\zeta_2\) are the real constants. We have explored all gathered
\(0<\zeta_1<\zeta_2\), \(\zeta_1<0<\zeta_2\), and \( \zeta_1<\zeta_2<0 \).
We extend the monotone iterative technique and establish the existence
results with reverse ordered upper and lower solutions to fourth-order
four-point non-linear BVPs.
Submitted March 17, 2023. Published August 4, 2023.
Math Subject Classifications: 34B10, 34B15, 34B16, 34B27, 34B60.
Key Words: Monotone iterative technique; upper solutions; lower solutions;
fourth-order; non-linear; four-point; Green's function.
DOI: https://doi.org/10.58997/ejde.2023.51
Show me the PDF file (450 KB), TEX file for this article.
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Nazia Urus Department of Mathematics IIT Patna, India email: nazia.pma17@iitp.ac.in |
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Amit K. Verma Department of Mathematics IIT Patna, India email: akverma@iitp.ac.in |
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