I'm interesting in neccesary and sufficient conditions for the equation $$x''+cx'+g(x)=p(t)$$ to have a periodic solution, where $g$ is strictly increasing, $c\neq 0$ and $p$ is continuous and $T$-periodic. Someone told me that what I was looking for: $$ \lim_{x\rightarrow - \infty} g(x) < \overline{p} <\lim_{x\rightarrow + \infty} g(x) $$ is a neccesary and sufficient condition, where $\overline{p} = \frac{1}{T}\int_0^T p(t)\ dt$. But he didn't tell where I could find this result.
Any idea of a book or paper that could be useful for me?
Thanks in advance.