The periodic problem for the second order integro-differential equations with distributed deviation

Abstract

We study the question of the unique solvability of the periodic type problem for the second order linear integro-differential equation with distributed argument deviation u"(t)=p_0(t)u(t)+\int_0^{\omega}p(t,s)u(\tau(t,s)) {\rm d}s+ q(t), and on the basis of the obtained results by the a priori boundedness principle we prove the new results on the solvability of periodic type problem for the second order nonlinear functional differential equations, which are close to the linear integro-differential equations. The proved results are optimal in some sense.

Keywords

• linear integro-differential equation
• periodic problem
• distributed deviation
• solvability