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

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.


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