A symmetric solution of a multipoint boundary value problem at resonance

Kosmatov, Nickolai

doi:https://doi.org/10.1155/AAA/2006/54121

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Volume 2006 | Article ID 054121 | https://doi.org/10.1155/AAA/2006/54121

A symmetric solution of a multipoint boundary value problem at resonance

Nickolai Kosmatov¹

Received18 Jan 2005

Accepted01 Jun 2005

Published23 Feb 2006

Abstract

We apply a coincidence degree theorem of Mawhin to show the existence of at least one symmetric solution of the nonlinear second-order multipoint boundary value problem u″(t)=f(t,u(t),|u′(t)|),t∈(0,1), u(0)=∑i=1nμiu(ξi),u(1−t)=u(t),t∈[0,1], where 0<ξ1<ξ2<…<ξn≤1/2, ∑i=1nμi=1, f:[0,1]×ℝ2→ℝ with f(t,x,y)=f(1−t,x,y), (t,x,y)∈[0,1]×ℝ2, satisfying the Carathéodory conditions.

References

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Copyright

Copyright © 2006 Nickolai Kosmatov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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