On t 2-like solutions of certain second order differential equations

Abstract

Via an integral transformation, we establish two embedding results between the Emden-Fowler type equationln(u−k) = c 1 < 0 for given k > 0. The conclusions of our investigation are used to derive conditions for the existence of radial solutions to the elliptic equation U = K(|x|)e U , |x| > x 0 > 0, that blow up as |x|x 0 in the two dimensional case.

Existence of unbounded positive solutions of quasilinear elliptic equations in two-dimensional exterior domains

“…For the discussion for the existence of bounded positive solutions of (1), we refer to [1][2][3][4][5]7,9,10,13,17,18]. By using Perron method, Yin [10] investigated the existence of unbounded positive solutions of (1) and obtained several good results.…”