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Iterated Hamiltonian type systems and applications. (English) Zbl 1382.37065

Summary: We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence, uniqueness and regularity properties, under the independence condition. We also investigate the critical case, define a class of generalized solutions and prove existence and basic properties. Relevant examples and counterexamples are also indicated. The applications concern representations of implicitly defined manifolds and their perturbations, motivated by differential systems involving unknown geometries.

MSC:

37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
26B10 Implicit function theorems, Jacobians, transformations with several variables
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
49K21 Optimality conditions for problems involving relations other than differential equations
49M37 Numerical methods based on nonlinear programming
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