## Applications of Schauder’s fixed point theorem to singular differential equations.(English)Zbl 1128.34027

The paper studies the existence of positive periodic solutions to the second-order singular differential equation $x''+a(t)x=f(t,x)+e(t),$ where $$a(t)$$ and $$e(t)$$ are continuous and $$1$$-periodic and $$f(t,x)$$ is $$1$$-periodic in $$t$$. The interest is focused on the case when $$f(t,x)$$ is singular at $$x=0$$. The proof relies on Schauder’s fixed point theorem. It is pointed out that in some situation weak singularities can help to create periodic solutions.

### MSC:

 34C25 Periodic solutions to ordinary differential equations 47H10 Fixed-point theorems
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