Decaying Solutions of Semilinear Elliptic Equations in ${\bf R}^N $

Abstract

This paper is concerned with the existence and asymptotic behavior of positive solutions of semilinear elliptic problems of second order in ${\bf R}^N $, $N \geqq 2$. Positive solutions in ${\bf R}^N $ that decay uniformly to zero at $\infty $ are obtained under various structure conditions by either a direct variational approach or a new approximation procedure. Sharp decay estimates are proved for two general classes of problems.