On solutions of one 6‐th order nonlinear boundary value problem - Garbuza, Tatjana (Mathematical Modelling and Analysis, 2008)
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