## Abstract and Applied Analysis

### Unbounded Solutions of Asymmetric Oscillator

#### Abstract

We obtain sufficient conditions for the existence of unbounded solutions of the following nonlinear differential equation ${({\phi }_{p}({x}^{\prime }))}^{\prime }+(p-1)[\alpha {\phi }_{p}({x}^{+})-\beta {\phi }_{p}({x}^{-})]=(p-1)f(t,x,{x}^{\prime })$, where ${\phi }_{p}(u)={|u|}^{p-2}u, p>1, {x}^{+}=\text{max}\{x,0\}, {x}^{-}=\text{max}\{-x,0\},\alpha ,\beta$ are positive constants, and $f$ is continuous, bounded, and $T$-periodic in $t$ for some $T>0$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 218346, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393443514

Digital Object Identifier
doi:10.1155/2013/218346

Mathematical Reviews number (MathSciNet)
MR3124074

Zentralblatt MATH identifier
1296.34083

#### Citation

Ji, Tieguo; Zhang, Zhenhui. Unbounded Solutions of Asymmetric Oscillator. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 218346, 6 pages. doi:10.1155/2013/218346. https://projecteuclid.org/euclid.aaa/1393443514

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