Geodesic
Entire solutions of semilinear elliptic equations
Electronic journal of differential equations, Tome 2004 (2004)
We consider existence of entire solutions of a semilinear elliptic equation $\Delta u= k(x) f(u)$ for $x \in \mathbb{R}^n, n\ge 3$. Conditions of the existence of entire solutions have been obtained by different authors. We prove a certain optimality of these results and new sufficient conditions for the nonexistence of entire solutions.
Classification : 35J60
Keywords: semilinear elliptic equation, entire solutions, nonexistence 
@article{EJDE_2004__2004__a12,
     author = {Gladkov,  Alexander and Slepchenkov,  Nickolai},
     title = {Entire solutions of semilinear elliptic equations},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1109.35044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a12/}
}
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%A Slepchenkov,  Nickolai
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Gladkov,  Alexander; Slepchenkov,  Nickolai. Entire solutions of semilinear elliptic equations. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a12/