## Abstract and Applied Analysis

### Antiperiodic Solutions for a Generalized High-Order $\left(p,q\right)$-Laplacian Neutral Differential System with Delays in the Critical Case

#### Abstract

By applying the method of coincidence degree, some criteria are established for the existence of antiperiodic solutions for a generalized high-order $\left(p,q\right)$-Laplacian neutral differential system with delays ${\left({\phi }_{p}\left({\left(x\left(t\right)-cx\left(t-\tau \right)\right)}^{\left(k\right)}\right)\right)}^{\left(m-k\right)}=F\left(t,{x}_{{\theta }_{\mathrm{0}}\left(t\right)},{x}_{{\theta }_{\mathrm{1}}\left(t\right)}^{\prime },\dots ,{x}_{{\theta }_{k}\left(t\right)}^{\left(k\right)},{y}_{{\vartheta }_{\mathrm{0}}\left(t\right)},{y}_{{\vartheta }_{\mathrm{1}}\left(t\right)}^{\prime },\dots ,{y}_{{\vartheta }_{l}\left(t\right)}^{\left(l\right)}\right)$, $\left({\phi }_{q}\left(\left(y\left(t\right)-$$dy\left(t-\sigma \right){\right)}^{\left(l\right)}\right){\right)}^{\left(n-l\right)}=G\left(t,{y}_{{\mu }_{\mathrm{0}}\left(t\right)},{y}_{{\mu }_{\mathrm{1}}\left(t\right)}^{\prime },\dots ,{y}_{{\mu }_{l}\left(t\right)}^{\left(l\right)},{x}_{{\nu }_{\mathrm{0}}\left(t\right)},{x}_{{\nu }_{\mathrm{1}}\left(t\right)}^{\prime },\dots ,{x}_{{\nu }_{k}\left(t\right)}^{\left(k\right)}\right)$ in the critical case $|c|=|d|=1$. The results of this paper are completely new. Finally, an example is employed to illustrate our results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 454619, 12 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511892

Digital Object Identifier
doi:10.1155/2013/454619

Mathematical Reviews number (MathSciNet)
MR3055956

Zentralblatt MATH identifier
1277.34101

#### Citation

Liao, Yongzhi; Zhang, Tianwei; Li, Yongkun. Antiperiodic Solutions for a Generalized High-Order $\left(p,q\right)$ -Laplacian Neutral Differential System with Delays in the Critical Case. Abstr. Appl. Anal. 2013 (2013), Article ID 454619, 12 pages. doi:10.1155/2013/454619. https://projecteuclid.org/euclid.aaa/1393511892