BOUNDARY FEATURES FOR AN ORDINARY DIFFERENTIAL EQUATION OF THE FOURTH ORDER
A nonlinear ordinary differential equation of the fourth order is considered, the solutions of which determine some states of elastic systems and phase states in the theory of crystals. From the solutions of this equation, we proceed to the consideration of the extremals of the functional. The problem of finding the extremals of the functional is reduced to finding the critical points of the main part of the key function obtained by the finite-dimensional reduction scheme. The imposition of additional restrictions on the considered function in the form of integral inequalities leads to the appearance of boundary features. All bif-decompositions arising for the key function are described. New bifurcation effects are found, which occur only in the presence of an edge.