Solutions of a multi-point boundary value problem for higher-order differential equations at resonance (III)

Authors

  • Yuji Liu
  • Weigao Ge

DOI:

https://doi.org/10.5556/j.tkjm.36.2005.124

Abstract

In this paper, we are concerned with the existence of solutions of the following multi-point boundary value problem consisting of the higher-order differential equations

$ x^{(n)}(t)=f(t,x(t),x'(t),\cdots,x^{(n-1)}(t))+e(t),\;\;0<1,\eqno{(\ast)} $

and the following multi-point boundary value conditions

$ \begin{array}{ll} x^{(i)}(0)=0\;\;for\;i=0,1,\cdots,n-3,\\ x^{(n-2)}(0)=\alpha x^{(n-1)}(\xi),\;\;x^{(n-1)}(1)=\beta x^{(n-2)}(\eta),\end{array} \eqno{(\ast\ast)} $

Sufficient conditions for the existence of at least one solution of the BVP$ (\ast) $ and $ (\ast\ast) $ at resonance are established. This paper is directly motivated by Liu and Yu [India J. Pure Appl. Math., 33(4)(2002)475-494] and Qi [Acta Math. Appl. Sinica, 17(2)(2001)271-278].

Author Biographies

Yuji Liu

Department of Applied Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan, 414000, P. R. China.

Weigao Ge

Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, P. R. China.

Downloads

Published

2005-06-30

How to Cite

Liu, Y., & Ge, W. (2005). Solutions of a multi-point boundary value problem for higher-order differential equations at resonance (III). Tamkang Journal of Mathematics, 36(2), 119–130. https://doi.org/10.5556/j.tkjm.36.2005.124

Issue

Section

Papers