Abstract and Applied Analysis

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

Yongzhi Liao, Tianwei Zhang, and Yongkun Li

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Abstract

By applying the method of coincidence degree, some criteria are established for the existence of antiperiodic solutions for a generalized high-order ( p , q ) -Laplacian neutral differential system with delays ( φ p ( ( x ( t ) - c x ( t - τ ) ) ( k ) ) ) ( m - k ) = F ( t , x θ 0 ( t ) , x θ 1 ( t ) , , x θ k ( t ) ( k ) , y ϑ 0 ( t ) , y ϑ 1 ( t ) , , y ϑ l ( t ) ( l ) ) , ( φ q ( ( y ( t ) - d y ( t - σ ) ) ( l ) ) ) ( n - l ) = G ( t , y μ 0 ( t ) , y μ 1 ( t ) , , y μ l ( t ) ( l ) , x ν 0 ( t ) , x ν 1 ( t ) , , x ν k ( t ) ( k ) ) 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

Permanent link to this document
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


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