Abstract:
The article considers a two-point boundary value problem for a fourth-order nonlinear ordinary differential equation, which describes the deformation of the equilibrium state of a beam, one end of which is rigidly fixed and the other is movable on a hinge. In the case of sublinear growth of the right side of the equation, using the Leray-Schauder theorem, the existence of a positive solution to the problem under consideration is established. To prove the uniqueness of a positive solution, a priori estimates of the solution and its derivatives.
Keywords:boundary Value Problem, positive Solution, green's function, leray-Schauder Theorem.
