Existence and controllability of integrodifferential equations with non-instantaneous impulses in Fréchet spaces

• Autores: Abdelhamid Bensalem, Abdelkrim Salim, Bashir Ahmad, Mouffak Benchohra
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 25, Nº. 2, 2023, págs. 231-250
• Idioma: inglés
• DOI: 10.56754/0719-0646.2502.231
• Enlaces
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• Resumen
  • español

    Resumen En este artículo, investigamos la existencia de soluciones mild de una ecuación integrodiferencial no-instantánea vía operadores resolventes en el sentido de Grimmer en espacios de Fréchet. Usando la técnica de medidas de nocompacidad junto con el teorema de punto fijo de Darbo, presentamos criterios suficientes para asegurar la controlabilidad del problema dado. Se discute, además, un ejemplo ilustrativo.

  • English

    Abstract In this paper, we investigate existence of mild solutions to a non-instantaneous integrodifferential equation via resolvent operators in the sense of Grimmer in Fréchet spaces. Utilizing the technique of measures of noncompactness in conjunction with the Darbo’s fixed point theorem, we present sufficient criteria ensuring the controllability of the given problem. An illustrative example is also discussed.

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