Bounded solutions to singularly perturbed systems of O. D. E

DOI10.1016/0022-0396(92)90125-7zbMath0762.34035OpenAlexW2036766673MaRDI QIDQ1201110

Claudio Lazzari, Flaviano Battelli

Publication date: 17 January 1993

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

Full work available at URL: https://doi.org/10.1016/0022-0396(92)90125-7

zbMATH Keywords

stabilityexistenceexponential dichotomybounded solutionssingularly perturbed systemMelnikov type function

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Growth and boundedness of solutions to ordinary differential equations (34C11) Singular perturbations for ordinary differential equations (34E15)

Related Items (4)

Symmetries and exponential smallness of bifurcation functions of a class of singular reversible systems ⋮ Chaos in singular impulsive O.D.E. ⋮ Bifurcation from homoclinic to periodic solutions in singularly perturbed differential inclusions ⋮ Exponential dichotomies and Melnikov functions for singularly perturbed systems

Cites Work

• Exponential dichotomies, heteroclinic orbits, and Melnikov functions
• Transversal heteroclinic and homoclinic orbits in singular perturbation problems
• Transversal heteroclinic points and Cherry's example of a nonintegrable Hamiltonian system
• Center manifolds and contractions on a scale of Banach spaces
• Applications of centre manifold theory
• Geometric singular perturbation theory for ordinary differential equations
• Dichotomies in stability theory
• Exponential dichotomies and transversal homoclinic points
• Dichotomies and stability in singularly perturbed systems of O.D.E.
• ON THE SMOOTHNESS OF THE COMPOSITION MAP
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