In this paper, we are concerned with the boundedness of all the solutions for a kind of second order differential equations with p-Laplacian and an oscillating term $(\phi_p(x'))'+a\phi_p(x^+)-b\phi_p(x^-)=G_x(x,t)+f(t)$, where$x^+=\max (x,0)$,$x^- =\max(-x,0)$,$\phi_p(s)=|s|^{ p-2}s$,$p\geq2$, $a $ and $b$ are positive constants $(a\not=b)$, the perturbation $f(t)\in { \cal C}^{ 23}(\RR/2\pi_p \ZZ)$, the oscillating term $G\in { \cal C}^{ 21}(\RR\times\RR/2\pi_p \ZZ)$,where $\pi_p=\frac{ 2\pi(p-1)^{ \frac{ 1}{ p}}}{ p\sin\frac{ \pi}{ p}},$ and $G(x,t)$ satisfies $\label{ G} |D_x^iD_t^jG(x,t)|\le C,\quad 0\le i+j\le 21,$ and $\label{ hatG} |D_t^j\hat{ G}|\le C,\quad 0\le j\le 21$ for some $C>0$, where $\hat{ G}$ is some function satisfying $\frac{ \pa \hat{ G}}{ \pa x}=G$.
Categories: math.DS math.CA