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This paper is concerned with periodic solutions of first-order nonlinear functional differential equations with deviating arguments. Some new sufficient conditions for the existence of periodic solutions are obtained. The paper extends and improves some well-known results.
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
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.
By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form
⎧y’(t) = A(t)y(t) + g(t,yt), , j ∈ ℤ,
⎨
⎩,
where is a nonsingular matrix with continuous real-valued entries.
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