Positive periodic solutions of first-order functional differential equations with parameter. (English) Zbl 1171.34342

Weng, Aizhi; Sun, Jitao

J. Comput. Appl. Math. 229, No. 1, 327-332 (2009).

Summary: We prove the existence and multiplicity of positive \(T\)-periodic solutions for the \(T\)-periodic equation
\[ x'(t)=h(t,x) - \lambda b(t)f(x(t -\tau (t))) \] by Krasnoselskii’s fixed point theorem, where \(f(x)\) may be singular at \(x=0\). Our results improve some recent results.

MSC:

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

Keywords:

periodic solution; fixed point theorem; existence; singularity

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