Existence and uniqueness results for fourth-order four-point bvp arising in bridge design in the presence of reverse ordered upper and lower solutions

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) & lambda;y''(s) = F(s, y(s)), s E (0, 1), y(0) = 0, y(1) = & delta;1y(& eta;1) + & delta;2y(& eta;2), y''(0) = 0, y''(1) = & delta;1y''(& eta;1) +& delta;2y''(& eta;2), where F E C([0, 1] x R, R), & delta;1, & delta;2 > 0, 0 < & eta;1 < & 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.