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

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]).