Electron. J. Differential Equations, Vol. 2023 (2023), No. 51, pp. 1-17.

Existence and uniqueness results for fourth-order four-point 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 fourth-order four-point non-linear boundary value problem (BVP) which arises in bridge design, −y(4)(s)−λy″(s)=F(s,y(s)),s∈(0,1),y(0)=0,y(1)=δ1y(η1)+δ2y(η2),y″(0)=0,y″(1)=δ1y″(η1)+δ2y″(η2), where F∈C([0,1]×R,R), δ1,δ2>0, 0<η1≤η2<1, λ=ζ1+ζ2, where ζ1 and ζ2 are the real constants. We have explored all gathered 0<ζ1<ζ2, ζ1<0<ζ2, and ζ1<ζ2<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.

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

Return to the EJDE web page