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
\[ u''(t)+a(t)u(t)=\lambda f(t,u(t-\tau_0(t)),u(t-\tau_1(t)),\dots,u(t-\tau_n(t))). \]
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)].


34K13 Periodic solutions to functional-differential equations
47H10 Fixed-point theorems
47N20 Applications of operator theory to differential and integral equations
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