## Odd periodic solutions of fully second-order ordinary differential equations with superlinear nonlinearities.(English)Zbl 1378.34065

Summary: This paper is concerned with the existence of periodic solutions for the fully second-order ordinary differential equation $u^{\prime\prime}(t) = f(t, u(t), u^{\prime}(t)), \quad t \in \mathbb{R},$ where the nonlinearity $$f : \mathbb{R}^3 \rightarrow \mathbb{R}$$ is continuous and $$f(t, x, y)$$ is $$2 \pi$$-periodic in $$t$$. Under certain inequality conditions such that $$f(t, x, y)$$ may have superlinear growth on $$(x, y)$$, the existence of odd $$2 \pi$$-periodic solutions is obtained via the Leray-Schauder fixed point theorem.

### MSC:

 34C25 Periodic solutions to ordinary differential equations 37C60 Nonautonomous smooth dynamical systems 47N20 Applications of operator theory to differential and integral equations

### Keywords:

superlinear growth; Leray-Schauder fixed point theorem
Full Text:

### References:

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