Electron. J. Differential Equations, Vol. 2023 (2023), No. 51, pp. 117.
Existence and uniqueness results for fourthorder fourpoint BVP arising
in bridge design in the presence of reverse ordered upper and lower solutions
Nazia Urus, Amit K. Verma
Abstract:
In this article, we establish the existence of solutions for a
fourthorder fourpoint nonlinear 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 fourthorder
fourpoint nonlinear 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;
fourthorder; nonlinear; fourpoint; Green's function.
DOI: https://doi.org/10.58997/ejde.2023.51
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Nazia Urus
Department of Mathematics
IIT Patna, India
email: nazia.pma17@iitp.ac.in


Amit K. Verma
Department of Mathematics
IIT Patna, India
email: akverma@iitp.ac.in

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