Periodic boundary-value problem for third-order linear functional differential equations

Abstract

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.