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.

Key words:

• nonlinear boundary value problem
• multiplicity of solutions
• oscillation
• differential equations of 6‐th order

Notes

Supported by ESF project Nr. 2004/0003/VPD1/ESF/PIAA/04/NP/3.2.3.1./0003/0065