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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2017, Volume 449, Issue 2, pp. 1570 - 1580
The Liénard equation is used in various applications. Therefore, constructing general analytical solutions of this equation is an important problem. Here we... 
Sundman transformation | Painlevé–Gambier classification | Liénard equation | Analytical solution | MATHEMATICS | Painleve-Gambier classification | LINEARIZATION | MATHEMATICS, APPLIED | INTEGRABILITY | Lienard equation | BEHAVIOR | SYSTEMS | ORDINARY DIFFERENTIAL-EQUATIONS
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 06/2017, Volume 27, Issue 6, p. 1750081
In this paper, we first present a survey of the known results on limit cycles and center conditions for Liénard differential systems. Next we propose a... 
Gröbner bases | analytic integrability | Center problem | Liénard differential systems | decomposition in prime ideals | Lienard differential systems | NUMBER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Grobner bases | MULTIDISCIPLINARY SCIENCES | LIMIT-CYCLES | CENTERS | POLYNOMIAL DIFFERENTIAL-SYSTEMS
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 09/2018, Volume 339, pp. 405 - 413
The key purpose of the present work is to constitute a numerical algorithm based on fractional homotopy analysis transform method to study the fractional model... 
Laplace transform | Fractional homotopy | Homotopy polynomials | Lienard's equation | Analysis | Algorithms
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 02/2019, Volume 45, pp. 542 - 556
In this paper, the problem of periodic solutions is studied for Liénard equations with anindefinite singularity x′′(t)+f(x(t))x′(t)+φ(t)xm(t)−α(t)xμ(t)=0,where... 
Singularity | Continuation theorem | Periodic solution | Liénard equation | EXISTENCE | MATHEMATICS, APPLIED | MOTION | MULTIPLICITY | Lienard equation | 2ND-ORDER DIFFERENTIAL-EQUATIONS | ATOM
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 08/2018, Volume 275, Issue 4, pp. 988 - 1007
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 07/2016, Volume 57, pp. 114 - 120
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 02/2018, Volume 76, pp. 208 - 214
The problem of uniqueness of limit cycles for the Liénard equation ẍ+f(x)ẋ+g(x)=0 is investigated. The classical assumption of sign-definiteness of f(x) is... 
Liénard equation | Limit cycles | Uniqueness | EXISTENCE | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | Lienard equation | THEOREM | SYSTEMS
Journal Article
Positivity, ISSN 1385-1292, 9/2019, Volume 23, Issue 4, pp. 779 - 787
Journal Article
Positivity, ISSN 1385-1292, 04/2019, Volume 23, Issue 2, pp. 431 - 444
In this paper, we consider the following quasilinear Lienard equation with a singularity where g has a attractive singularity at the origin and satisfies... 
Superlinear | Attractive singularity | Periodic solution | Liénard equation | MATHEMATICS | PERIODIC-SOLUTIONS | Lienard equation | Information science
Journal Article
Theoretical and Mathematical Physics, ISSN 0040-5779, 8/2018, Volume 196, Issue 2, pp. 1230 - 1240
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 10/2018, Volume 84, pp. 124 - 129
A. M. Lyapunov proved the inequality that makes it possible to estimate the distance between two consecutive zeros a and b of solutions of a linear... 
The Van der Pol equation with relativistic acceleration | Relativistic equation | Lyapunov-type inequality | EXISTENCE | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | LIENARD EQUATIONS | PENDULUM | PHI-LAPLACIAN | Differential equations
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 06/2019, Volume 29, Issue 6, p. 1950074
A dynamical system possessing an equilibrium point with two zero eigenvalues is considered. We assume that a degenerate Bogdanov–Takens bifurcation with... 
Heteroclinic orbit | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | double-zero bifurcation with symmetry of order two | Lienard equation | MULTIDISCIPLINARY SCIENCES | regular perturbation method | CONNECTIONS
Journal Article
Regular and Chaotic Dynamics, ISSN 1560-3547, 7/2015, Volume 20, Issue 4, pp. 486 - 496
Journal Article
by Lu, SP and Xue, RY
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, ISSN 1230-3429, 09/2019, Volume 54, Issue 1, pp. 203 - 218
In this paper, the existence of positive periodic solutions is studied for a singular Lienard equation where the weight function has an indefinite sign. Due to... 
periodic solution | EXISTENCE | MATHEMATICS | Lienard equation | 2ND-ORDER DIFFERENTIAL-EQUATIONS | Mawhin's continuation theorem | singularity
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2011, Volume 250, Issue 4, pp. 2162 - 2176
Based on geometric singular perturbation theory we prove the existence of classical Liénard equations of degree 6 having 4 limit cycles. It implies the... 
Singular perturbations | Relaxation oscillation | Limit cycles | Classical Liénard equations | Slow–fast system | Slow-fast system | MATHEMATICS | Classical Lienard equations
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 04/2019, Volume 346, pp. 183 - 192
A periodic problem of Ambrosetti–Prodi type is studied in this paper for the Liénard equation with a singularity of attractive... 
Multiplicity result | Singularity | Periodic solutions | Liénard equation | Upper and lower functions | MATHEMATICS, APPLIED | Lienard equation | 2ND-ORDER DIFFERENTIAL-EQUATIONS | NONLINEAR PERTURBATIONS
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 02/2015, Volume 25, Issue 2, pp. 1550032 - 1-1550032-11
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 12/2015, Volume 82, Issue 4, pp. 1953 - 1968
In this paper we develop a systematic and self-consistent procedure based on a set of compatibility conditions for identifying all maximal (eight parameter)... 
Liénard-type equation | Engineering | Vibration, Dynamical Systems, Control | Lie point symmetries | Mechanics | Ordinary differential equations | Automotive Engineering | Mechanical Engineering | Parameter identification | Hamiltonian functions | Mathematical analysis | Integral equations | Symmetry
Journal Article
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 08/2017, Volume 22, Issue 6, pp. 2465 - 2478
Using a novel transformation involving the Jacobi Last Multiplier (JLM) we derive an old integrability criterion due to Chiellini for the Lienard equation. By... 
Iscochronous system | Metriplectic structure | Complex Hamiltonization | Chiellini integrabilty condition | Liénard equation | MATHEMATICS, APPLIED | iscochronous system | Lienard equation | metriplectic structure | LAST MULTIPLIER | complex Hamiltonization | FORMULATION
Journal Article
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