Stability And Boundedness In Nonlinear And Neutral Difference Equations using New Variation of Parameters Formula And Fixed Point Theory

• Autores: Youssef N. Raffoul
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 21, Nº. 3, 2019, págs. 39-61
• Idioma: inglés
• DOI: 10.4067/S0719-06462019000300039
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen En el caso de problemas no-lineales, ya sea en ecuaciones diferenciales o en diferencias, es difícil y en algunos casos imposible invertir el problema y obtener una aplicación apropiada que pueda ser efectivamente usada en teoría de punto fijo para analizar quantitativamente sus soluciones. En este paper consideramos la existencia de una sucesión positiva y la usamos en la capacidad del factor de integración para obtener una nueva fórmula de variación de parámetros. Luego, usaremos esta nueva fórmula de variación de parámetros y volver al principio de contracción para obtener resultados que involucran acotamiento, periodicidad y estabilidad. El autor se encuentra trabajando en resultados paralelos para el caso continuo

  • English

    Abstract In the case of nonlinear problems, whether in differential or difference equations, it is difficult and in some cases impossible to invert the problem and obtain a suitable mapping that can be effectively used in fixed point theory to qualitatively analyze its solutions. In this paper we consider the existence of a positive sequence and utilize it in the capacity of integrating factor to obtain a new variation of parameters formula. Then, we will use the obtained new variation of parameters formula and revert to the contraction principle to arrive at results concerning, boundedness, periodicity and stability. The author is working on parallel results for the continuous case.

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