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2013 BOUNDEDNESS FOR SECOND ORDER DIFFERENTIAL EQUATIONS WITH JUMPING $p$-LAPLACIAN AND AN OSCILLATING TERM
Xiao Ma, Daxiong Piao, Yiqian Wang
Taiwanese J. Math. 17(6): 1945-1966 (2013). DOI: 10.11650/tjm.17.2013.3108

Abstract

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 $x^+ = \max (x,0)$, $x^- = \max(-x,0)$, $\phi_p(s) = |s|^{p-2}s$, $p \geq 2$, $a$ and $b$ are positive constants $(a\not=b)$, the perturbation $f(t) \in {\cal C}^{23}(\mathbb{R}/2\pi_p \mathbb{Z})$, the oscillating term $G\in {\cal C}^{21}(\mathbb{R} \times \mathbb{R}/2\pi_p \mathbb{Z})$ satisfying $\label{G} |D_x^iD_t^jG(x,t)|\le C,\quad 0\le i+j\le 21$.

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Xiao Ma. Daxiong Piao. Yiqian Wang. "BOUNDEDNESS FOR SECOND ORDER DIFFERENTIAL EQUATIONS WITH JUMPING $p$-LAPLACIAN AND AN OSCILLATING TERM." Taiwanese J. Math. 17 (6) 1945 - 1966, 2013. https://doi.org/10.11650/tjm.17.2013.3108

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1288.34034
MathSciNet: MR3141868
Digital Object Identifier: 10.11650/tjm.17.2013.3108

Subjects:
Primary: 34C55 , 70H08

Keywords: $p$-Laplace equations , boundedness of solutions , canonical transformation , method of principle integral , Moser's small twist theorem , oscillating term

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 6 • 2013
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