chapter  30
7 Pages

On Positive Solutions of the Equation Δ U + f ( | x | ) U p = 0   in   ℝ n , n > 2


Positive solutions of the problem (E) below when f is nonnegative and decreasing have been investigated thoroughly by many authors (see references herein). Here we provide some sufficient conditions for their existence even in some cases where f (or f′) changes sign. Some estimates of the solutions are provided.