Existence and uniqueness results for fourth-order four-point BVP arising in bridge design in the presence of reverse ordered upper and lower solutions
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, $$\displaylines{ - y^{(4)}( s)-\lambda y''( s)=\mathcal{F}( s, y( s)), \quad s\in(0,1),\cry(0)=0,\quad y(1)= \delta_1 y(\eta_1)+\delta_2 y(\eta_2),\cr y''(0)=0,\quad y''(1)= \delta_1 y''(\eta_1)+\delta_2 y''(\eta_2), }$$ where \(\mathcal{F} \in C([0,1]\times \mathbb{R},\mathbb{R})\), \(\delta_1, …