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On one two-point BVP for the fourth order linear ordinary differential equation

  • Sulkhan Mukhigulashvili EMAIL logo and Mariam Manjikashvili

Abstract

In this article we consider the two-point boundary value problem

{u(4)(t)=p(t)u(t)+h(t)for atb,u(i)(a)=c1i,u(i)(b)=c2i(i=0,1),

where c1i,c2iR, h,pL([a,b];R). Here we study the question of dimension of the space of nonzero solutions and oscillatory behaviors of nonzero solutions on the interval [a,b] for the corresponding homogeneous problem, and establish efficient sufficient conditions of solvability for the nonhomogeneous problem.

MSC 2010: 34B05; 34C10; 34C30

Dedicated to Professor Ivan Kiguradze on the occasion of his 80th birthday


Funding statement: The research was supported by the Czech Science Foundation. Name of the project: “Development of new methods of solving dynamic models of corporate processes management”. Project No.: GA16-03796S.

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Received: 2016-9-26
Accepted: 2016-11-4
Published Online: 2017-2-25
Published in Print: 2017-6-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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