ON THE SOLVABILITY OF HAMILTON'S EQUATIONS IN HILBERT SPACES

DOI10.1142/S0219025703001092zbMath1069.34084OpenAlexW2067050732MaRDI QIDQ3043496

Stanislav Shkarin

Publication date: 6 August 2004

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025703001092

zbMATH Keywords

existenceCauchy problemHamilton equationPeano theoremsquare-summable sequencesordinary differential equation in a Hilbert space

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear differential equations in abstract spaces (34G20) Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems (37K99)

Cites Work

• Unnamed Item
• Sull'esistenza delle soluzioni delle equazioni differenziali ordinarie in forma implicita negli spazi di Banach
• Peano's theorem in an infinite-dimensional Hilbert space is false even in a weakened formulation
• Peano's theorem in Banach spaces
• Counterexample to Peano's theorem in infinite-dimensional \(F'\)-spaces
• Ordinary differential equations with a continuous right-hand side in Fréchet spaces
• Peano's theorem fails for infinite-dimensional Fréchet spaces
• On the nonexistence of solutions of differential equations in nonreflexive spaces
• On Lipschitz conditions for ordinary differential equations in Fréchet spaces

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