A Cantilever Beam Problem with Small Deflections and Perturbed Boundary Data

Abstract

The boundary value problem of a fourth-order beam equation u4=λfx,u,u′,u″,u′′′,0≤x≤1 is investigated. We formulate a nonclassical cantilever beam problem with perturbed ends. By determining appropriate values of λ and estimates for perturbation measurements on the boundary data, we establish an existence theorem for the problem under integral boundary conditions u0=u′0=∫01pxuxdx,u″1=u′′′1=∫01qxu″xdx, where p,q∈L10,1, and f is continuous on 0,1×0,∞×0,∞×−∞,0×−∞,0.