ON SOLUTIONS OF ONE 6‐TH ORDER NONLINEAR BOUNDARY VALUE PROBLEM

Abstract

A special technique based on the analysis of oscillatory behaviour of linear equations is applied to investigation of a nonlinear boundary value problem of sixth order. We get the estimation of the number of solutions to boundary value problems of the type x(6) = f(t, x), x(a) = A, x′ (a) = A 1, x″(a) = A 2, x′″(a) = A 3, x(b) = B, x′(b) = B1 , where f is continuous together with the partial derivative f′x which is supposed to be positive. We assume also that at least one solution of the problem under consideration exists.