Upper and lower solutions for φ-laplacian third-order bvps on the half line

• Smaïl Djebali ^[1] ; Ouiza Saifi ^[2]
  1. [1] École Normale Supérieure
  2. [2] Algiers University 3 Faculty of Economic and Management Sciences Department of Economics
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 16, Nº. 1, 2014, págs. 105-116
• Idioma: inglés
• DOI: 10.4067/S0719-06462014000100010
• Enlaces
  • Texto completo
• Resumen
  • español

    En este artículo investigamos la existencia de una solución positiva de una clase de problema singular de valores de frontera de tercer-orden asociado con el operador Φ-Laplaciano y colocado sobre la semirecta real positiva: donde μ > 0. Usando la técnica de sub y súper soluciones y la teoría del punto fijo, se prueba la existencia de soluciones positivas bajo una condición de monotonicidad sobre f. La nolinealidad f puede ser singular en x = 0. Se incluye un ejemplo de aplicación para ilustrar el resultado principal de existencia.

  • English

    In this paper, we investigate the existence of positive solution for a class of singular third-order boundary value problem associated with a Φ-Laplacian operator and posed on the positive half-line: where μ > 0. By using the upper and lower solution approach and the fixed point theory, the existence of positive solutions is proved under a monotonic condition on f. The nonlinearity f may be singular at x = 0. An example of application is included to illustrate the main existence result.

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