Quasi-periodic solutions for p-Laplacian equations with jumping nonlinearity and unbounded potential terms

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 $(ϕ_p(x'))'+aϕ_p(x^+)-bϕ_p(x^-)+f(x)=e(t)$, where $x^+=\max (x,0)$, $x^- =\max(-x,0)$, $ϕ_p(s)=|s|^{p-2}s$, $p\geq2$, $a$ and $b$ are positive constants $(a\not=b)$, and satisfy $\frac{1}{a^{\frac{1}{p}}}+\frac{1}{b^{\frac{1}{p}}}=2ω^{-1}$,where $ω\in \RR^+ \backslash \QQ$, the perturbation $f$ is unbounded, $e(t)\in {\cal C}^{6}$ is is a smooth $2π_p$-periodic function on $t$, where $π_p=\frac{2π(p-1)^{\frac{1}{p}}}{p\sin\fracπ{p}}$.

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