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Existence nonexistence and multiplicity of periodic solutions for a kind of functional differential equation with parameter. (English) Zbl 1166.34038

The author obtains some results on the existence, nonexistence and multiplicity of positive periodic solutions for a family of functional periodic differential equations of second order of the form

u '' (t)+a(t)u(t)=λf(t,u(t-τ 0 (t)),u(t-τ 1 (t)),,u(t-τ n (t)))·

The main tool used is the Krasnoselkii fixed point theorem in cones. For closely related results, see, e.g. [H. Y. Wang, J. Differ. Equations 202, No. 2, 354–366 (2004; Zbl 1064.34052)], [Y. Wu, Nonlinear Anal., Theory Methods Appl. 68, No. 7(A), 1954–1962 (2008; Zbl 1146.34049)].

34K13Periodic solutions of functional differential equations
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47N20Applications of operator theory to differential and integral equations