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Mechanical interpretation of existence theorems in a nonlinear Dirichlet problem.

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Title: Mechanical interpretation of existence theorems in a nonlinear Dirichlet problem.
Authors: González, Augusto1 agonzale@icmf.inf.cu
Source: Revista Cubana de Física. 2007, Vol. 24 Issue 2, p144-149. 6p. 7 Graphs.
Subjects: EXISTENCE theorems, NONLINEAR statistical models, DIRICHLET problem, VISCOSITY, QUALITATIVE research
Abstract (English): The existence of radial solutions to a nonlinear Dirichlet problem in a ball is translated to the language of Mechanics, i.e. to requirements on the time of motion of a particle in an external potential and under the action of a viscosity force. This approach provides a qualitative, but rigorous, method for the analysis of the general case. Known theorems are easily reproduced and examples of new theorems are given, which prove the usefulness of this qualitative method. [ABSTRACT FROM AUTHOR]
Abstract (Spanish): La existencia de soluciones radiales a un problema de Dirichlet no lineal en una región esférica es traducida al lenguaje de la Mecánica, es decir se expresa como requerimientos sobre el tiempo en que se mueve una partícula en un potencial externo y sujeta a la acción de una fuerza viscosa. Esta forma de abordar el problema nos brinda un método cualitativo, pero riguroso, de analizar el caso general. Teoremas conocidos son fácilmente reproducidos. Se dan ejemplos de nuevos teoremas, los cuales prueban la utilidad de este método cualitativo. [ABSTRACT FROM AUTHOR]
Copyright of Revista Cubana de Física is the property of Universidad de La Habana and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Label: Title
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  Data: Mechanical interpretation of existence theorems in a nonlinear Dirichlet problem.
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  Data: <searchLink fieldCode="AR" term="%22González%2C+Augusto%22">González, Augusto</searchLink><relatesTo>1</relatesTo><i> agonzale@icmf.inf.cu</i>
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  Data: <searchLink fieldCode="JN" term="%22Revista+Cubana+de+Física%22">Revista Cubana de Física</searchLink>. 2007, Vol. 24 Issue 2, p144-149. 6p. 7 Graphs.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22EXISTENCE+theorems%22">EXISTENCE theorems</searchLink><br /><searchLink fieldCode="DE" term="%22NONLINEAR+statistical+models%22">NONLINEAR statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22DIRICHLET+problem%22">DIRICHLET problem</searchLink><br /><searchLink fieldCode="DE" term="%22VISCOSITY%22">VISCOSITY</searchLink><br /><searchLink fieldCode="DE" term="%22QUALITATIVE+research%22">QUALITATIVE research</searchLink>
– Name: Abstract
  Label: Abstract (English)
  Group: Ab
  Data: The existence of radial solutions to a nonlinear Dirichlet problem in a ball is translated to the language of Mechanics, i.e. to requirements on the time of motion of a particle in an external potential and under the action of a viscosity force. This approach provides a qualitative, but rigorous, method for the analysis of the general case. Known theorems are easily reproduced and examples of new theorems are given, which prove the usefulness of this qualitative method. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label: Abstract (Spanish)
  Group: Ab
  Data: La existencia de soluciones radiales a un problema de Dirichlet no lineal en una región esférica es traducida al lenguaje de la Mecánica, es decir se expresa como requerimientos sobre el tiempo en que se mueve una partícula en un potencial externo y sujeta a la acción de una fuerza viscosa. Esta forma de abordar el problema nos brinda un método cualitativo, pero riguroso, de analizar el caso general. Teoremas conocidos son fácilmente reproducidos. Se dan ejemplos de nuevos teoremas, los cuales prueban la utilidad de este método cualitativo. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Revista Cubana de Física is the property of Universidad de La Habana and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 6
        StartPage: 144
    Subjects:
      – SubjectFull: EXISTENCE theorems
        Type: general
      – SubjectFull: NONLINEAR statistical models
        Type: general
      – SubjectFull: DIRICHLET problem
        Type: general
      – SubjectFull: VISCOSITY
        Type: general
      – SubjectFull: QUALITATIVE research
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      – TitleFull: Mechanical interpretation of existence theorems in a nonlinear Dirichlet problem.
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              M: 07
              Text: 2007
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              Y: 2007
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