Existence of positive entire solutions of semilinear elliptic equations

Abstract

For n ≥ 3 and p > 1 , the elliptic equation Δ u + K ( x ) u p + f ( x ) = 0 in R n possesses a positive entire solution under proper conditions on locally Hölder continuous functions K and f . After obtaining a priori estimates on decay of solutions near ∞ , we study the existence of positive solutions, and present necessary conditions of f for the existence.