Asymptotic behaviour of the wronskian of boundary condition functions for a fourth order boundary value problem (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: π : Lφ ≡ φ (4) ( x) + P2 (x) φ (2) ( x) + P3 (x) φ (1) ( x) + P4 (x) φ (x) = λφ (x) φ (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 πF given by πF : φ (4) ( x) = λφ (x), φ (a) = φ / (a) = φ (b) = φ / (b) = 0. AMS Subject Classifcation: 35B40, 34B05