Attractive singularity problems for superlinear Liénard equation (Q2424866)

The paper deals with the quasilinear Liénard equation with a singularity \[ (\phi_{p}(x'))'+f(x)x'+g(t,x)=e(t), \] where $\phi_{p}(s)=|s|^{p-2}s$ with $p>1$, $f\in\mathcal{C}(\mathbb{R})$, $g\in\mathcal{C}(\mathbb{R}\times\mathopen{]}0,+\infty\mathclose{[})$ is a $T$-periodic function in $t$ and has a singularity at $x=0$ and has superlinear growth at $x=+\infty$. $e\in\mathcal{C}(\mathbb{R})$ is a $T$-periodic function with zero mean value. They apply a result by \textit{R. Manásevich} and \textit{J. Mawhin} [J. Differ. Equations 145, No. 2, 367--393 (1998; Zbl 0910.34051)] to obtain existence of at least a positive $T$-periodic solution. The paper ends with an application of the main theorem.