An elliptic equation with random potential and supercritical nonlinearity

Abstract

espanolEstamos interesados en una ecuacion eliptica no homogenea con potencial aleatorio y no linealidad supercritica. Obtenemos la existencia de solucion casi seguramente para una clase de potenciales que incluye continuos y discretos. Ademas, proporcionamos una ley de grandes numeros para las soluciones obtenidas por conjuntos independientes y estimamos el valor esperado para sus normas L∞. EnglishWe are concerned with a nonhomogeneous elliptic equation with random potential and supercritical nonlinearity. Existence of solution is obtained almost surely for a class of potentials that includes continuum and discrete ones. Also, we provide a law of larger numbers for the obtained solutions by independent ensembles and estimate the expected value for their L∞-norms.