Boundedness for second order differential equations with jumping \(p\)-Laplacian and an oscillating term (Q395632)

Motivated by a previous paper by \textit{B. Liu} [J. Differ. Equations 207, No. 1, 73--92 (2004; Zbl 1069.34052)] the authors consider the differential equation NEWLINE\[NEWLINE(\phi_p (x'))'+a\phi_p (x^+ )-b\phi_p (x^- )=G_x (x,t)+f(t)NEWLINE\]NEWLINE where \(\phi_p (s)=|s|^{p-2} s\). They assume that the number NEWLINE\[NEWLINE\omega =\frac{1}{2} \left(\frac{1}{a^{1/p}} +\frac{1}{b^{1/p}} \right)NEWLINE\]NEWLINE satisfies a Diophantine condition and impose some assumptions on the functions \(G\) and \(f\) in order to deduce that all solutions are bounded.