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Singularities of Singular Solutions of First-Order Differential Equations of Clairaut Type

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Abstract

A first-order differential equation of Clairaut type has a family of classical solutions, and a singular solution when the contact singular set is not empty. The projection of a singular solution of Clairaut type is an envelope of a family of fronts (Legendre immersions). In these cases, the envelopes are always fronts. We investigate singular points of envelopes for first-order ordinary differential equations, first-order partial differential equations, and systems of first-order partial differential equations of Clairaut type, respectively.

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Authors and Affiliations

  1. Department of Mathematics, Kobe University, Kobe, 657-8501, Japan

    Kentaro Saji

  2. Muroran Institute of Technology, Muroran, 050-8585, Japan

    Masatomo Takahashi

Authors
  1. Kentaro Saji
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  2. Masatomo Takahashi
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Correspondence to Masatomo Takahashi.

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The first author was a partially supported by JSPS KAKENHI Grant Number JP 18K03301. The second author was a partially supported by JSPS KAKENHI Grant Numbers JP 17K05238 and 20K03573.

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Saji, K., Takahashi, M. Singularities of Singular Solutions of First-Order Differential Equations of Clairaut Type. J Dyn Control Syst 28, 19–41 (2022). https://doi.org/10.1007/s10883-020-09511-4

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  • DOI: https://doi.org/10.1007/s10883-020-09511-4

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