In this paper we study the behavior near infinity of non-negative solutions of the semi-linear elliptic equation
where and . Especially, for a non-negative radial solution of this equation we prove the following alternative:
either has a compact support
or tends to one at infinity.
Moreover, we prove that if a general solution is sufficiently small in some sense, then it is compactly supported. To prove this result we use some inequalities between the solution and its spherical average at a shift point and consider a differential inequality. Finally, we prove the existence of non-trivial solutions which converge to one at infinity.
Cite this article
Michèle Grillot, Philippe Grillot, Asymptotical Behavior of Solutions of Nonlinear Elliptic Equations in . Z. Anal. Anwend. 20 (2001), no. 4, pp. 915–928DOI 10.4171/ZAA/1051