• Previous Article
    Polarization dynamics during takeover collisions of solitons in systems of coupled nonlinears Schödinger equations
  • PROC Home
  • This Issue
  • Next Article
    Wavelet analysis of phase clusters in a distributed biochemical system
2011, 2011(Special): 1395-1403. doi: 10.3934/proc.2011.2011.1395

Stability, boundedness and uniform boundedness of solutions of nonlinear delay differential equations

1. 

Department of Mathematics, Faculty of Sciences, Yüzüncü Yil University, 65080, Van, Turkey

Received  June 2010 Revised  April 2011 Published  October 2011

In this paper, we consider a Lienard equation with multiple variable deviating arguments. By using the Lyapunov second (direct) method, we discuss the stability, boundedness and uniform boundedness of solutions of the equation considered. An example is given to illustrate the feasibility of the proposed results.
Citation: Cemil Tunç. Stability, boundedness and uniform boundedness of solutions of nonlinear delay differential equations. Conference Publications, 2011, 2011 (Special) : 1395-1403. doi: 10.3934/proc.2011.2011.1395
[1]

Cyrine Fitouri, Alain Haraux. Boundedness and stability for the damped and forced single well Duffing equation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 211-223. doi: 10.3934/dcds.2013.33.211

[2]

Mats Gyllenberg, Yan Ping. The generalized Liénard systems. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 1043-1057. doi: 10.3934/dcds.2002.8.1043

[3]

Na Li, Maoan Han, Valery G. Romanovski. Cyclicity of some Liénard Systems. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2127-2150. doi: 10.3934/cpaa.2015.14.2127

[4]

Alina Gleska, Małgorzata Migda. Qualitative properties of solutions of higher order difference equations with deviating arguments. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 239-252. doi: 10.3934/dcdsb.2018016

[5]

Nguyen Thieu Huy, Vu Thi Ngoc Ha, Pham Truong Xuan. Boundedness and stability of solutions to semi-linear equations and applications to fluid dynamics. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2103-2116. doi: 10.3934/cpaa.2016029

[6]

A. Ghose Choudhury, Partha Guha. Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Liénard equation. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2465-2478. doi: 10.3934/dcdsb.2017126

[7]

Renato Manfrin. On the boundedness of solutions of the equation $u''+(1+f(t))u=0$. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 991-1008. doi: 10.3934/dcds.2009.23.991

[8]

Masaki Kurokiba, Toshitaka Nagai, T. Ogawa. The uniform boundedness and threshold for the global existence of the radial solution to a drift-diffusion system. Communications on Pure & Applied Analysis, 2006, 5 (1) : 97-106. doi: 10.3934/cpaa.2006.5.97

[9]

Ming Mei, Yau Shu Wong, Liping Liu. Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (I) Existence and uniform boundedness. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 825-837. doi: 10.3934/dcdsb.2007.7.825

[10]

Wenting Cong, Jian-Guo Liu. Uniform $L^{∞}$ boundedness for a degenerate parabolic-parabolic Keller-Segel model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 307-338. doi: 10.3934/dcdsb.2017015

[11]

Fuchen Zhang, Xiaofeng Liao, Chunlai Mu, Guangyun Zhang, Yi-An Chen. On global boundedness of the Chen system. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1673-1681. doi: 10.3934/dcdsb.2017080

[12]

Jaume Llibre, Claudia Valls. On the analytic integrability of the Liénard analytic differential systems. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 557-573. doi: 10.3934/dcdsb.2016.21.557

[13]

Bin Liu. Quasiperiodic solutions of semilinear Liénard equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (1) : 137-160. doi: 10.3934/dcds.2005.12.137

[14]

Robert Roussarie. Putting a boundary to the space of Liénard equations. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 441-448. doi: 10.3934/dcds.2007.17.441

[15]

Patricia J.Y. Wong. On the existence of fixed-sign solutions for a system of generalized right focal problems with deviating arguments. Conference Publications, 2007, 2007 (Special) : 1042-1051. doi: 10.3934/proc.2007.2007.1042

[16]

Masaaki Mizukami. Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2301-2319. doi: 10.3934/dcdsb.2017097

[17]

Wenbin Liu, Zhaosheng Feng. Periodic solutions for $p$-Laplacian systems of Liénard-type. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1393-1400. doi: 10.3934/cpaa.2011.10.1393

[18]

Isaac A. García, Jaume Giné, Jaume Llibre. Liénard and Riccati differential equations related via Lie Algebras. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2/3, September) : 485-494. doi: 10.3934/dcdsb.2008.10.485

[19]

Fangfang Jiang, Junping Shi, Qing-guo Wang, Jitao Sun. On the existence and uniqueness of a limit cycle for a Liénard system with a discontinuity line. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2509-2526. doi: 10.3934/cpaa.2016047

[20]

Jitsuro Sugie, Tadayuki Hara. Existence and non-existence of homoclinic trajectories of the Liénard system. Discrete & Continuous Dynamical Systems - A, 1996, 2 (2) : 237-254. doi: 10.3934/dcds.1996.2.237

 Impact Factor: 

Metrics

  • PDF downloads (0)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]