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- W2000633808 abstract "In this paper we study the behavior near infinity of non-negative solutions $u in C^2(mathbb R^N)$ of the semi-linear elliptic equation $$ – Delta u+u^q – u^p =0 $$ where $q in (0, 1), p > q$ and $N ≥2$. Especially, for a non-negative radial solution of this equation we prove the following alternative: either $u$ has a compact support or $u$ 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." @default.
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- W2000633808 date "2001-01-01" @default.
- W2000633808 modified "2023-10-18" @default.
- W2000633808 title "Asymptotical Behavior of Solutions of Nonlinear Elliptic Equations in $R^N$" @default.
- W2000633808 doi "https://doi.org/10.4171/zaa/1051" @default.
- W2000633808 hasPublicationYear "2001" @default.
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