The method of lower and upper solutions and the stability of periodic oscillations

DOI10.1016/S0362-546X(01)00888-4zbMath1043.34044OpenAlexW1998795513MaRDI QIDQ1849030

Daniel E. Nuñez

Publication date: 28 November 2002

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(01)00888-4

zbMATH Keywords

stabilitylower and upper solutionsperiodic oscillations

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability of solutions to ordinary differential equations (34D20) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (9)

Stable odd solutions of some periodic equations modeling satellite motion. ⋮ Twist periodic solutions of repulsive singular equations ⋮ Twist periodic solutions in the relativistic driven harmonic oscillator ⋮ Lyapunov stability of elliptic periodic solutions of nonlinear damped equations ⋮ Stable periodic solutions in the forced pendulum equation ⋮ On the stability of periodic solutions with defined sign in MEMS via lower and upper solutions ⋮ On the motion of an oscillator with a periodically time-varying mass ⋮ Twist character of the fourth order resonant periodic solution ⋮ Existence and stability of periodic oscillations of a rigid dumbbell satellite around its center of mass

Cites Work

• An example of a Schrödinger equation with almost periodic potential and nowhere dense spectrum
• The twist coefficient of periodic solutions of a time-dependent Newton's equation
• The index of Lyapunov stable fixed points in two dimensions
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Periodic solutions of a Newtonian equation: Stability by the third approximation
• The stability of the equilibrium of a conservative system
• Topological Degree and Stability of Periodic Solutions for Certain Differential Equations
• The Stability of the Equilibrium of a Nonlinear Hill’s Equation
• Boundedness and global asymptotic stability of a forced oscillator
• Parabolic fixed points and stability criteria for nonlinear Hill's equation
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