Properties of bounded solutions of linear and nonlinear evolution equations: Homoclinics of a beam equation

DOI10.1016/0022-0396(87)90159-8zbMath0639.35007OpenAlexW2041828155MaRDI QIDQ1100338

B. George

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0022-0396(87)90159-8

zbMATH Keywords

homoclinic solutionssemigroup theorybounded solutionsbeam equationheteroclinic solutionsLyapunov-Schmidt procedure

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Stability in context of PDEs (35B35) Nonlinear differential equations in abstract spaces (34G20) Bifurcations in context of PDEs (35B32) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Related Items (12)

Abstract methods for synchronization and applications ⋮ The Hartman-Grobman theorem for reversible systems on Banach spaces ⋮ On the relationship between exponential dichotomies and the Fredholm alternative ⋮ On the Hartman-Grobman theorem with parameters ⋮ Dynamics of a class of ODEs more general than almost periodic ⋮ Robustness of nonuniform exponential dichotomies in Banach spaces ⋮ Fredholm operators and nonuniform exponential dichotomies ⋮ On exponential decay and the Markus-Yamabe conjecture in infinite dimensions with applications to the Cima system ⋮ Nonuniform exponential dichotomies and Fredholm operators for flows ⋮ Existence of nonuniform exponential dichotomies and a Fredholm alternative ⋮ Bifurcation of periodics and subharmonics in abstract nonlinear undamped wave equations ⋮ Invariant foliations for parabolic equations

Cites Work

• Semigroups of linear operators and applications to partial differential equations
• Exponential dichotomies and homoclinic orbits in functional differential equations
• Heteroclinic orbits for retarded functional differential equations
• An example of bifurcation to homoclinic orbits
• Geometric theory of semilinear parabolic equations
• Smoothness of bounded solutions of nonlinear evolution equations
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