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Periodic solutions of a second order ordinary differential equation: A necessary and sufficient condition for nonresonance. (English) Zbl 0743.34045
The paper considers the periodic problem $$-x''=f(x)x'+g(x)+h(t)$$ in $$[0,2\pi]$$; $$x(0)=x(2\pi)$$, $$x'(0)=x'(2\pi)$$; $$f$$ and $$g$$ continuous from $$\mathbb{R}$$ to $$\mathbb{R}$$ and $$h\in L^ \infty(0,2\pi)$$. The author proves the existence of at least one solution if $$\lim\sup g(s)/s$$ and $$\lim\sup(2/s^ 2)\int^ s_ 0g(r) dr$$ are appropriately bounded for $$s\to\pm\infty$$ and if there exist $$A$$ and $$B$$ in $$\mathbb{R}$$ such that $$g(A)\leq-h(t)\leq g(B)$$.

##### MSC:
 34C25 Periodic solutions to ordinary differential equations
##### Keywords:
periodic solution; nonresonance
Full Text:
##### References:
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