Global Asymptotic Stability of a Generalized Liénard Equation

Abstract

Previous article Global Asymptotic Stability of a Generalized Liénard EquationJ. W. HeidelJ. W. Heidelhttps://doi.org/10.1137/0119061PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] T. A. Burton, The generalized Lienard equation, J. Soc. Indust. Appl. Math. Ser. A Control, 3 (1965), 223–230 MR0190462 0135.30201 LinkGoogle Scholar[2] Philip Hartman, Ordinary differential equations, John Wiley & Sons Inc., New York, 1964xiv+612 MR0171038 0125.32102 Google Scholar[3] Joseph LaSalle and , Solomon Lefschetz, Stability by Liapunov's direct method, with applications, Mathematics in Science and Engineering, Vol. 4, Academic Press, New York, 1961vi+134 MR0132876 0098.06102 Google Scholar[4] D. W. Willett and , J. S. W. Wong, The boundedness of solutions of the equation $\ddot x+f(x,\dot x)+g(x)=0$, SIAM J. Appl. Math., 14 (1966), 1084–1098 10.1137/0114087 MR0208091 0173.34703 LinkISIGoogle Scholar[5] Philip Hartman, On an ordinary differential equation involving a convex function, Trans. Amer. Math. Soc., 146 (1969), 179–202 MR0276539 0196.10703 CrossrefISIGoogle Scholar Previous article FiguresRelatedReferencesCited byDetails Stability analysis and synthesis of stabilizing controls for a class of nonlinear mechanical systems5 June 2020 | Nonlinear Dynamics, Vol. 100, No. 4 Cross Ref Qualitative analysis for a variable delay system of differential equations of second order23 March 2019 | Journal of Taibah University for Science, Vol. 13, No. 1 Cross Ref Discrete Dynamics in Nature and Society, Vol. 2018 Cross Ref ALMOST AUTOMORPHIC DYNAMICS OF GENERALIZED LIÉNARD EQUATIONJournal of Applied Analysis & Computation, Vol. 7, No. 1 Cross Ref Boundedness of Solutions to a Certain System of Differential Equations with Multiple Delays29 January 2016 Cross Ref On the instability of solutions to a Liénard type equation with multiple deviating arguments15 June 2013 | Afrika Matematika, Vol. 25, No. 4 Cross Ref Stability to vector Liénard equation with constant deviating argument5 January 2013 | Nonlinear Dynamics, Vol. 73, No. 3 Cross Ref On the stability and boundedness of solutions of a class of nonautonomous differential equations of second order with multiple deviating arguments1 July 2011 | Afrika Matematika, Vol. 23, No. 2 Cross Ref New stability and boundedness results of Liénard type equations with multiple deviating arguments1 September 2010 | Journal of Contemporary Mathematical Analysis, Vol. 45, No. 4 Cross Ref Oscillations for Liénard type equationsJournal de Mathématiques Pures et Appliquées, Vol. 90, No. 1 Cross Ref Stability and boundedness properties of certain second-order differential equationsJournal of the Franklin Institute, Vol. 344, No. 5 Cross Ref On the asymptotic behavior of solutions of certain second-order differential equationsJournal of the Franklin Institute, Vol. 344, No. 5 Cross Ref Boundedness criteria for solutions of certain second order nonlinear differential equationsJournal of Mathematical Analysis and Applications, Vol. 123, No. 2 Cross Ref Comparison Theorems for Matrix Riccati EquationsRobert A. Jones12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 29, No. 1AbstractPDF (1020 KB)Stability Properties of a Second Order Damped and Forced Nonlinear Differential EquationJohn W. Baker12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 27, No. 1AbstractPDF (766 KB)On Global Asymptotic Stability of Certain Second Order Differential Equations with Integrable Forcing TermsLouis H. Thurston and James S. W. Wong17 February 2012 | SIAM Journal on Applied Mathematics, Vol. 24, No. 1AbstractPDF (975 KB)On the generalized Liénard equation with negative dampingJournal of Differential Equations, Vol. 12, No. 1 Cross Ref A Liapunov function for a generalized Liénard equationJournal of Mathematical Analysis and Applications, Vol. 39, No. 1 Cross Ref Oscillation of solutions of a generalized Liénard equation1 January 1972 | Proceedings of the American Mathematical Society, Vol. 33, No. 1 Cross Ref Structure of the solution set of some first order differential equations of comparison type1 January 1971 | Transactions of the American Mathematical Society, Vol. 160, No. 0 Cross Ref Volume 19, Issue 3| 1970SIAM Journal on Applied Mathematics History Submitted:21 October 1969Published online:12 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0119061Article page range:pp. 629-636ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics