Applications of generic bifurcation. I

DOI10.1007/BF00249688zbMath0328.47036OpenAlexW4234996098MaRDI QIDQ1226748

John Mallet-Paret, Shui-Nee Chow, Jack K. Hale

Publication date: 1975

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00249688

Mathematics Subject Classification ID

Equations involving nonlinear operators (general) (47J05) Periodic solutions to PDEs (35B10) Spectral theory and eigenvalue problems for partial differential equations (35P99) Plates (74K20) Nonlinear elliptic equations (35J60) First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65)

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Cites Work

• Unnamed Item
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• An existence theorem for periodically perturbed conservative systems
• Periodically perturbed conservative systems
• Integral averaging and bifurcation
• On the inversion of some differentiable mappings with singularities between Banach spaces
• Alternative problems for nonlinear functional equations
• Topological models in Biology
• The bifurcation of one or more closed orbits from an equilibrium point of an autonomous differential system
• On periodically perturbed conservative systems
• On nonuniqueness of solutions of the von Kármán equations
• Functional analysis and Galerkin's method
• Bifurcation from simple eigenvalues
• Topics in stability and bifurcation theory
• Periodic Solutions of Nonlinear Hyperbolie Partial Differential Equations
• On von kármán's equations and the buckling of a thin elastic plate, I the clamped plate
• Von Kármán's equations and the buckling of a thin elastic plate, II plate with general edge conditions
• Generic one-parameter families of vector fields on two-dimensional manifolds
• Application of a Lemma on Bilinear Forms to a Problem in Nonlinear Oscillations
• The Hopf bifurcation for nonlinear semigroups
• Soluzioni periodiche di equazioni a derivate parziali di tipo iperbolico non lineari
• Perturbed bifurcation theory