Positive solutions of nabla fractional boundary value problem

• Autores: N. S. Gopal, Jagan Mohan Jonnalagadda
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 3, 2022, págs. 467-484
• Idioma: inglés
• DOI: 10.56754/0719-0646.2403.0467
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen En este artículo consideramos el siguiente problema de valor en la frontera de dos puntos discreto fraccional con coeficientes constantes asociado a condiciones de frontera de tipo Dirichlet donde 1 < ν < 2, a, b ∈ ℝ con b −a ∈ ℕ3, = {a+2, a+3, . . . , b}, |λ| < 1, denota la nabla diferencia de Riemann-Liouville de u de orden ν basada en ρ(a) = a − 1, y f: × ℝ → ℝ+. Usamos los teoremas de punto fijo de Guo-Krasnosels’kiĭ y Leggett-Williams en conos adecuados y bajo condiciones apropiadas en la parte nolineal de la ecuación en diferencias. Establecemos requerimientos suficientes para al menos una, al menos dos, y al menos tres soluciones positivas del problema de valor en la frontera considerado. También entregamos un ejemplo para mostrar la aplicabilidad de los resultados.

  • English

    Abstract In this article, we consider the following two-point discrete fractional boundary value problem with constant coefficient associated with Dirichlet boundary conditions. where 1 < ν < 2, a, b ∈ ℝ with b −a ∈ ℕ3, = {a+2, a+3, . . . , b}, |λ| < 1, denotes the ν th-order Riemann-Liouville nabla difference of u based at ρ(a) = a − 1, and f: × ℝ → ℝ+. We make use of Guo-Krasnosels’kiĭ and Leggett-Williams fixed-point theorems on suitable cones and under appropriate conditions on the non-linear part of the difference equation. We establish sufficient requirements for at least one, at least two, and at least three positive solutions of the considered boundary value problem. We also provide an example to demonstrate the applicability of established results.

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