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.

First Published Online: 14 Oct 2010