This paper deals with the existence of periodic solutions for some partial functional differential equations with infinite delay. We suppose that the linear part is nondensely defined and satisfies the Hille᎐Yosida condition. In the nonlinear case we give several criteria to ensure the existence of a periodic solution. In the nonhomogeneous linear case, we prove the existence of a periodic solution under the existence of a bounded solution. ᮊ 2001 Academic Press t 1 Ž . dt ¢ x s g B B, 0
We study the existence of a periodic solution for some partial functional differential equations. We assume that the linear part is nondensely defined and satisfies the Hille-Yosida condition. In the nonhomogeneous linear case, we prove the existence of a periodic solution under the existence of a bounded solution. In the nonlinear case, using a fixed-point theorem concerning set-valued maps, we establish the existence of a periodic solution.
SynopsisWe present a new result on the existence of periodic solutions for the equation:for all positive parameters λ sufficiently large. Our fundamental assumption is the following monotonicity property: if ø ≧ ψ (ø and ψ are data) then x(ø) ≧ x(ψ). The proof consists in applying the global Hopf bifurcation theorem. The main steps are: (i) a classical estimation of the periods; (ii) an a priori estimate for the solutions along a connected branch; (iii) a transformation acting on periodic solutions.
In this paper we give necessary and sufficient conditions for the existence of periodic solutions for convex functional differential equations of neutral type with finite and infinite delay. ᮊ
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