Existence of at least two periodic solutions of the forced relativistic pendulum

DOI10.1090/S0002-9939-2011-11101-8zbMath1275.34057OpenAlexW1968560637MaRDI QIDQ2845545

Pedro J. Torres, Cristian Bereanu

Publication date: 2 September 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-11101-8

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Periodic solutions to ordinary differential equations (34C25) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50)

Related Items (14)

Twist periodic solutions in the relativistic driven harmonic oscillator ⋮ On the existence of periodic oscillations for pendulum-type equations ⋮ Radial solutions of Neumann problem for periodic perturbations of the mean extrinsic curvature operator ⋮ Relativistic type systems with parametric odd nonlinearities ⋮ Relativistic pendulum and invariant curves ⋮ Periodic solutions to differential equations with a generalized \(p\)-Laplacian ⋮ Existence and stability of periodic solutions for relativistic singular equations ⋮ On Littlewood's boundedness problem for relativistic oscillators with singular potentials ⋮ A global solution curve for a class of periodic problems, including the relativistic pendulum ⋮ Prevalence of stable periodic solutions in the forced relativistic pendulum equation ⋮ Homoclinic solutions for a class of relativistic Liénard equations ⋮ On the periodic solutions of the relativistic driven harmonic oscillator ⋮ Periodic Solutions of Differential and Difference Systems with Pendulum-Type Nonlinearities: Variational Approaches ⋮ Existence and multiplicity results for some nonlinear problems with singular \(\phi\)-Laplacian via a geometric approach

Cites Work

• Variational methods for nonlinear perturbations of singular \(\varphi \)-Laplacians
• Periodic solutions of the forced relativistic pendulum
• Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations
• A general mountain pass principle for locating and classifying critical points
• Functional analysis, Sobolev spaces and partial differential equations
• On the use of asymptotics in nonlinear boundary value problems
• Extensions of the mountain pass theorem
• Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems
• A deformation theorem and some critical point results for non-differentiable functions
• Radial solutions of Neumann problems involving mean extrinsic curvature and periodic nonlinearities
• Existence and multiplicity results for some nonlinear problems with singular \(\phi\)-Laplacian
• MULTIPLE BOUNDED VARIATION SOLUTIONS OF A PERIODICALLY PERTURBED SINE-CURVATURE EQUATION
• Radial solutions for Neumann problems involving mean curvature operators in Euclidean and Minkowski spaces

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