Existence of periodic solutions of Duffing equations

DOI10.1016/0022-0396(89)90073-9zbMath0676.34025OpenAlexW2064675643MaRDI QIDQ1122693

Gerhard Metzen, Patrick Habets

Publication date: 1989

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(89)90073-9

zbMATH Keywords

resonance problems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25)

Related Items (25)

Jumping nonlinearities for neumann BVPs with positive forcing ⋮ Nonselfadjoint 4th order boundary value problems ⋮ Inequalities verified by asymmetric nonlinear operators ⋮ Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities ⋮ A \(p\)-Laplacian problem with a multi-point boundary condition ⋮ A continuation approach to superlinear periodic boundary value problems ⋮ Nonresonance conditions on the potential with respect to the Fučik spectrum for the periodic boundary value problem ⋮ Numerical solution of Duffing equation by using an improved Taylor matrix method ⋮ Periodic solutions for Duffing equations ⋮ Generalized upper and lower solution method for the forced Duffing equation ⋮ On the number of solutions of a Duffing equation ⋮ On equivalent conditions for the solvability of the equation \((p(t)x')'+f(t,x)=h(t)\) satisfying linear boundary conditions with \(f\) restricted by linear growth conditions ⋮ Periodic solutions of Liénard equations with superlinear asymmetric nonlinearities. ⋮ A nonconvex dissipative system and its applications. I ⋮ Periodic solutions of asymptotically positively homogeneous differential equations ⋮ Sublinear impulse effects and solvability of boundary value problems for differential equations with impulses ⋮ Periodic solutions for second order differential inclusions with the scalar \(p\)-Laplacian ⋮ Invariance of homotopy and an extension of a theorem by Habets-Metzen on periodic solutions of Duffing equations ⋮ On the Existence of Stable Periodic Solutions of Differential Equations of Duffing Type ⋮ Nonresonance conditions for asymptotically positively homogeneous differential systems: The Fučik spectrum and its generalization ⋮ Nonuniform nonresonance of semilinear differential equations ⋮ Existence of Periodic Solutions of Second Order Differential Equations with Delay ⋮ Periodic solutions of nonlinear differential equations with double resonance ⋮ Periodic solutions for second order differential equations ⋮ Monotonous property of non-oscillations of the damped Duffing's equation

Cites Work

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• Nonuniform nonresonance conditions at the two first eigenvalues for periodic solutions of forced Liénard and Duffing equations
• A Multiplicity Result for Periodic Solutions of Forced Nonlinear Second order Ordinary Differential Equations
• Existence Results on the One-Dimensional Dirichlet Problem Suggested by the Piecewise Linear Case
• Resonance problems with nonlinearity interfering with eigenvalues of higher order^heigen
• Perturbations of second order linear elliptic problems by nonlinearities without landesman-lazer condition
• On the Dirichlet problem for weakly non-linear elliptic partial differential equations
• On the periodic BVP for the forced duffing equation with jumping nonlinearity

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