Positive solutions of some elliptic differential equations with oscillating nonlinearity

Abstract

We discuss the occurrence of positive solutions which decay to 0 as vertical bar xj vertical bar ->+infinity the differential equation Delta u+f(x, u)+g(vertical bar x vertical bar)x . del u=0, vertical bar xj vertical bar>R>0, x is an element of R-n, where n >= 3, g is nonnegative valued and f has alternating sign, by means of the comparison method. Our results complement several recent contributions from Ehrnstrom and Mustafa [ M. Ehrnstrom, O.G. Mustafa, On positive solutions of a class of nonlinear elliptic equations, Nonlinear Anal. TMA 67 (2007), pp. 1147-1154].