Bounded and Periodic Solutions of Integral Equations

• T. A Burton ^[1] ; Bo Zhang ^[2]
  1. [1] Northwest Research Institute
  2. [2] University Fayetteville Department of Mathematics and Computer Science Fayetteville State
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 14, Nº. 1, 2012, págs. 55-79
• Idioma: inglés
• DOI: 10.4067/S0719-06462012000100006
• Enlaces
  • Texto completo
• Resumen
  • español

    En este artículo presentamos un nuevo método para obtener acotación de soluciones de ecuaciones integrales. A partir de la ecuación integral, formamos una ecuación integrales diferencial calculando x’ + kx mediante la aplicación de un funcional de Liapunov. Ello puede resultar bastante más efectivo que la técnica usual de diferenciación de la ecuación. Las propiedades cualitativas derivadas de la ecuación son entonces transferidas a la función mayorante para la ecuación integral. El teorema del punto fijo de Schaefer es usado para concluir que hay una solución periódica. Se estudia tres tipos de ecuaciones integrales y se muestra que ellas están relacionadas a través de dos ejemplos.

  • English

    In this paper we introduce a new method for obtaining boundedness of solutions of integral equations. From the integral equation we form an integrodifferential equation by computing x’ + kx to which we apply a Liapunov functional. This can be far more effective than the usual technique of differentiating the equation. The qualitative properties derived from that equation are then transferred to a majorizing function for the integral equation. Schaefer’s fixed point theorem is used to conclude that there is a periodic solution. Three kinds of integral equations are studied and they are shown to be related through two examples.

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