Boundary Value Problems 
Volume 2005 (2005), Issue 3, Pages 247-261
doi:10.1155/BVP.2005.247

On a periodic boundary value problem for second-order linear functional differential equations

S. Mukhigulashvili1,2

1A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Aleksidze Street 1, Tbilisi 0193, Georgia
2Mathematical Institute, Academy of Sciences of the Czech Republic, Žižkova 22, Brno 616 62, Czech Republic

Received 26 October 2004; Revised 7 March 2005

Abstract

Unimprovable efficient sufficient conditions are established for the unique solvability of the periodic problem u″(t)=ℓ(u)(t)+q(t) for 0≤t≤ω, u(i)(0)=u(i)(ω)(i=0,1), where ω>0, ℓ:C([0,ω])→L([0,ω]) is a linear bounded operator, and q∈L([0,ω]).