A Liapunov function for a generalized Lienard equation

DOI10.1016/0022-247X(72)90234-XzbMath0243.34096MaRDI QIDQ2554457

J. W. Heidel

Publication date: 1972

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10)

Related Items

Boundedness criteria for solutions of certain second order nonlinear differential equations ⋮ On the generalized Liénard equation without the signum condition ⋮ On the asymptotic behavior of solutions of certain second-order differential equations ⋮ On the necessary and sufficient conditions for the boundedness of the solutions of the nonlinear oscillating equation ⋮ Boundedness of solutions of nonlinear systems of differential equations ⋮ Stability to vector Liénard equation with constant deviating argument ⋮ Boundedness of solutions for some nonlinear differential systems ⋮ Global asymptotic stability of nonautonomous systems of Liénard type. ⋮ On the boundedness and the attractivity properties of nonlinear second order differential equations ⋮ On the boundedness of the solutions of the nonlinear oscillating equation ⋮ A NOTE ON PERIODIC SOLUTIONS OF A FORCED LIÉNARD-TYPE EQUATION ⋮ On the attractivity properties for the equation x + a(t)f//1(x)g//1(x')x' + b(t)f//2(x)g//2(x')x = e(t,x,x') ⋮ Further results on the boundedness and the attractivity properties of nonlinear second order differential equations ⋮ Boundedness of solutions for a class of nonlinear planar systems.

Cites Work

• Stability by Liapunov's direct method. With applications
• Stability theory for ordinary differential equations
• On the equation \(x +f(x)h(x')x' +g(x) = e(t)\)
• The Generalized Lienard Equation
• The Boundedness of Solutions of the Equation $\ddot x + f( {x,\dot x} ) + g( x ) = 0$
• Global Asymptotic Stability of a Generalized Liénard Equation
• On Non-Linear Differential Equations of the Second Order with Integrable Forcing Term^†