arXiv subjects

Daxiong Piao

Publications and source records attributed to Daxiong Piao.

22 records · Page 2Linked to original sources

arXiv2013

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 $π_p=\frac{2π(p-1)^{\frac{1}{p}}}{p\sin\fracπ{p}}$.

math.DS↗

arXiv2013

Bounded and Almost Periodic Solutions for Second Order Differential Equation Involving Reflection of the Argument

In this paper we investigate the existence and uniqueness of bounded, periodic and almost periodic solutions for second order differential equations involving reflection of the argument.The relationship between frequency modules of forced term and the solution of the equation is considered.

math.CA↗

arXiv2013

Boundedness of solutions for a class of impact oscillators with time-denpendent polynomial potentials

In this paper, we consider the boundedness of solutions for a class of impact oscillators $$ \{{array}{ll} \displaystyle \ddot{x}+x^{2n+1}+\sum_{i=0}^{2n}p_{i}(t)x^{i}=0,& \quad {\rm for}\quad x(t)> 0, x(t)\geq 0,& \dot{x}(t_{0}^{+})=-\dot{x}(t_{0}^{-}),& \quad {\rm if}\quad x(t_{0})=0, {array}. $$ where $n\in\NN^{+}$, $p_{i}(t+1)=p_{i}(t)$ and $p_{i}(t)\in C^5(\RR/\ZZ).$

math.DS↗

arXiv2013

Boundedness for Second Order Differential Equations with Jumping p-Laplacian and an Oscillating Term

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 $(ϕ_p(x'))'+aϕ_p(x^+)-bϕ_p(x^-)=G_x(x,t)+f(t)$, where$x^+=\max (x,0)$,$x^- =\max(-x,0)$,$ϕ_p(s)=|s|^{p-2}s$,$p\geq2$, $a $ and $b$ are positive constants $(a\not=b)$, the perturbation $f(t)\in {\cal C}^{23}(\RR/2π_p \ZZ)$, the oscillating term $G\in {\cal C}^{21}(\RR\times\RR/2π_p \ZZ)$,where $π_p=\frac{2π(p-1)^{\frac{1}{p}}}{p\sin\fracπ{p}},$ 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 $\frac{\pa \hat{G}}{\pa x}=G$.

math.DS↗