On the buckling of a column in an elastic medium

One deals with the buckling of a cantilever column in an elastic medium by the aid of the differential eqns (2), (2′) with bilocal conditions (3), (3′). Introducing the conventional load (4), one considers the three cases P_cr < P₀, P_cr = P₀ and P_cr > P₀ and one determines the corresponding characteristics eqns (8″), (12), (15″). The reduced critical load P_cr/P₎ and the reduced critical length l_cr/l are listed in a table and plotted into diagrams for various values of an adimensional magnitude bl. One obtains also the asymptotic formulae (16), (16′).