Asymptotic Behaviour of the Wronskian of Boundary Condition Functions for a Fourth Order Boundary Value Roblem (A Special Case)

Abstract

In this paper, we prove that the Wronskian W (λ) of the boundary condition functions for the following boundary value problem π:a) = φ / (a) = φ (b) = φ / (b) = 0 is asymptotically equivalent for large values of |λ|, to the Wronskian of the boundary condition functions of the corresponding Fourier problem π F given by π F : φ (4) (x) = λφ (x) , φ (a) = φ / (a) = φ (b) = φ / (b) = 0.