In this paper, we are concerned with the boundedness of all the solutions for a kind of second order differential equations with p-Laplacian term $(\phi_p(x'))'+a\phi_p(x^+)-b\phi_p(x^-)+f(x)=e(t)$, where $x^+=\max (x,0)$, $x^- =\max(-x,0)$, $\phi_p(s)=|s|^{ p-2}s$, $p\geq2$, $a$ and $b$ are positive constants $(a\not=b)$, and satisfy $\frac{ 1}{ a^{ \frac{ 1}{ p}}}+\frac{ 1}{ b^{ \frac{ 1}{ p}}}=2\omega^{ -1} $,where $\omega \in \RR^+ \backslash \QQ$, the perturbation $f$ is unbounded, $e(t)\in { \cal C}^{ 6}$ is is a smooth $2\pi_p$-periodic function on $t$, where $\pi_p=\frac{ 2\pi(p-1)^{ \frac{ 1}{ p}}}{ p\sin\frac{ \pi}{ p}}$.
Categories: math.DS