Approximate controllability of non-instantaneous impulsive stochastic integrodifferential equations driven by Rosenblatt process via resolvent operators

• Autores: Essozimna Kpizim, Bertin Dehigbe, Ramkumar Kasinathan, Ravikumar Kasinathan, Mamadou Abdoul Diop
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 25, Nº. 3, 2023, págs. 467-495
• Idioma: inglés
• DOI: 10.56754/0719-0646.2503.467
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen En este trabajo investigamos la existencia de una solución mild y la controlabilidad aproximada de ecuaciones integro-diferenciales estocásticas no-instantáneas impulsivas dirigidas por el proceso de Rosenblatt en espacios de Hilbert con el parámetro de Hurst H ∈ (1/2, 1). Logramos este resultado usando la teoría de semigrupos de operadores lineales acotados, la teoría del operador resolvente de Grimmer y análisis estocástico. Usando los teoremas de punto fijo de Krasnoselskii y Schauder, demostramos la existencia de soluciones mild y la controlabilidad aproximada del sistema. Finalmente, un ejemplo muestra el potencial para resultados significativos.

  • English

    Abstract In this work, we investigate the existence of a mild solution and the approximate controllability of non-instantaneous impulsive stochastic integrodifferential equations driven by the Rosenblatt process in Hilbert space with the Hurst parameter H ∈ (1/2, 1). We achieve the result using the semigroup theory of bounded linear operators, Grimmer’s resolvent operator theory, and stochastic analysis. Using Krasnoselskii’s and Schauder’s fixed point theorems, we demonstrate the existence of mild solutions and the approximate controllability of the system. Finally, an example shows the potential for significant results.

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