A Cantilever Beam Problem with Small Deflections and Perturbed Boundary Data. (8th November 2021) - Khanfer, Ammar
Abstract : The boundary value problem of a fourth-order beam equation u 4 = λ f x, 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 u 0 = u ′ 0 = ∫ 0 1 p x u x d x, u ″ 1 = u ′ ′ ′ 1 = ∫ 0 1 q x u ″ x d x, where p, q ∈ L 1 0, 1, and f is continuous on 0, 1 × 0, ∞ × 0, ∞ × − ∞, 0 × − ∞, 0 .