Periodic boundary-value problem for third-order linear functional differential equations - Hakl, R. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
For the linear functional differential equation of the third order u’’’ (t) = l(u)(t) + q(t), theorems on the existence and uniqueness of a solution satisfying the conditions u( i)(0) = u( i), i=0,1,2, are established. Here, l is a linear continuous operator transforming the space C([0, ω];R) into the space L([0, ω];R), and q ∈ L([0, ω];R). The question on the nonnegativity of a solution of the considered boundary-value problem is also studied.