## Positive periodic solutions of second-order differential equations.(English)Zbl 1127.34325

The authors consider the second-order nonlinear differential equation $x''(t)+a(t)x'(t)+f(t,x(t))=0,$ where $$a(t)\in C(\mathbb{R},\mathbb{R})$$, $$a(t+\omega)\equiv a(t)$$, $$f(t,u)\in C(\mathbb{R}\times\mathbb{R},\mathbb{R})$$, $$f(t+\omega,u)\equiv f(t,u)$$ and investigate existence of positive periodic solutions using a fixed point theorem for cones [see e.g. D. Guo and V. Lakshmikantham, Nonlinear problems in abstract cones. Boston, MA: Academic Press (1988; Zbl 0661.47045) or K. Deimling, Nonlinear Functional Analysis. Berlin etc.: Springer (1985; Zbl 0559.47040)]. They extend some of results achieved by Y. Li [Chin. Ann. Math., Ser. B 25, No. 3, 413–420 (2004; Zbl 1073.34041)], where criteria for existence of positive periodic solutions of the equation $x''(t)+f(t,x(t))=0,$ are proved.

### MSC:

 34C25 Periodic solutions to ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations

### Citations:

Zbl 0661.47045; Zbl 0559.47040; Zbl 1073.34041
Full Text:

### References:

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