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Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations

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  • Yuri E. Gliklikh

Abstract

We derive necessary and sufficient conditions for global-in-time existence of solutions of ordinary differential, stochastic differential, and parabolic equations. The conditions are formulated in terms of complete Riemannian metrics on extended phase spaces (conditions with two-sided estimates) or in terms of derivatives of proper functions on extended phase spaces (conditions with one-sided estimates).

Suggested Citation

  • Yuri E. Gliklikh, 2006. "Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-17, April.
    • Handle: RePEc:hin:jnlaaa:039786
    DOI: 10.1155/AAA/2006/39786
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    Cited by:

    1. Francisco Beltran-Carbajal & Hugo Yañez-Badillo & Ruben Tapia-Olvera & Julio C. Rosas-Caro & Carlos Sotelo & David Sotelo, 2023. "Neural Network Trajectory Tracking Control on Electromagnetic Suspension Systems," Mathematics, MDPI, vol. 11(10), pages 1-26, May.

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