Stability properties of periodic solutions of a Duffing equation in the presence of lower and upper solutions.

DOI10.1016/S0096-3003(02)00062-0zbMath1034.34060OpenAlexW2171339743MaRDI QIDQ1856003

Pierpaolo Omari, Franic Ikechukwu Njoku

Publication date: 28 January 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(02)00062-0

zbMATH Keywords

periodic solutionslower and upper solutionsasymptotic stabilitytopological degreeDuffing equationantimaximum principle

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability of solutions to ordinary differential equations (34D20) Perturbations of ordinary differential equations (34D10)

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The rate of decay of stable periodic solutions for Duffing equation with \(L^p\)-conditions ⋮ On the pumping effect in a pipe/tank flow configuration with friction ⋮ Dynamics of a fluid equation with Neumann boundary conditions ⋮ Asymptotically stable non-falling solutions of the Kapitza-Whitney pendulum ⋮ Exact multiplicity and stability of periodic solutions for a Duffing equation ⋮ Mathematical analysis of a model for moon-triggered clumping in Saturn's rings ⋮ Unnamed Item ⋮ Singularly perturbed higher order periodic boundary value problems. ⋮ Novel existence and uniqueness criteria for periodic solutions of a Duffing type \(p\)-Laplacian equation ⋮ Three solutions for forced Duffing-type equations with damping term ⋮ Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities ⋮ Exact multiplicity and stability of periodic solutions for Duffing equation with bifurcation method ⋮ Stability analysis in some strongly prestressed rectangular plates ⋮ Existence results for damped regular equations under periodic or Neumann boundary conditions

Cites Work

• Remarks on the lower and upper solutions method for second- and third- order periodic boundary value problems
• On the number of solutions for the forced pendulum equation
• The index of Lyapunov stable fixed points in two dimensions
• Periodic solutions of a Newtonian equation: Stability by the third approximation
• Dynamics of a periodic differential equation with a singular nonlinearity of attractive type
• On the Existence of Stable Periodic Solutions of Differential Equations of Duffing Type
• Periodic Solutions of some Lienard Equations with Singularities
• Topological Degree and Stability of Periodic Solutions for Certain Differential Equations
• Existence of asymptotically stable periodic solutions of a forced equation of Lienard type
• Bounded solutions in singular equations of repulsive type
• On Periodic Solutions of Nonlinear Differential Equations with Singularities
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