Ukr. Mat. Zh. - 2008. - 60, № 3. - pp. 413–425
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.