Existence of Entire Solutions for Quasilinear Elliptic Systems under Keller-Osserman Condition
نویسندگان
چکیده
In this paper, we study the existence of entire solutions for the following elliptic system △mu = p(x)f(v),△lv = q(x)g(u), x ∈ R, where 1 < m, l < ∞, f, g are continuous and non-decreasing on [0,∞), satisfy f(t) > 0, g(t) > 0 for all t > 0 and the Keller-Osserman condition. We establish conditions on p and q that are necessary for the existence of positive solutions, bounded and unbounded, of the given equation. RESUMEN En este art́ıculo estudiamos la existencia de soluciones enteras para el siguiente sistema eĺıptico △mu = p(x)f(v),△lv = q(x)g(u), x ∈ R, donde 1 < m, l < ∞, f, g son continuas y no-decrecientes en [0,∞), satisfaciendo f(t) > 0, g(t) > 0 para todo t > 0 y la condición de Keller-Osserman. Establecemos condiciones sobre p y qy que son necesarias para la existencia de soluciones positivas, acotadas y no acotadas de la ecuación dada.
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