Semilinear elliptic equations for the fractional Laplacian involving critical exponential growth

2016 ◽  
Vol 40 (5) ◽  
pp. 1757-1772 ◽  
Author(s):  
Manassés de Souza ◽  
Yane Lisley Araújo
Keyword(s):  
Exponential Growth ◽  
Elliptic Equations ◽  
Fractional Laplacian ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Critical Exponential Growth

Singular solutions of semilinear elliptic equations with fractional Laplacian in entire space

2016 ◽  
Vol 18 (01) ◽  
pp. 1550024 ◽  
Author(s):  
Zhuoran Du
Keyword(s):  
Elliptic Equations ◽  
Singular Solution ◽  
Fractional Laplacian ◽  
Semilinear Elliptic Equations ◽  
Singular Solutions ◽  
Entire Space ◽  
Semilinear Elliptic ◽  
Supercritical Exponent ◽  
Extension Result

We consider the existence of positive singular solutions of the problem [Formula: see text] where [Formula: see text] and [Formula: see text]. We obtain the existence of positive singular solutions [Formula: see text] of this problem in space dimensions [Formula: see text] for the case [Formula: see text] under the condition [Formula: see text]. By the well-known Caffarelli–Silvestre extension result, the trace of [Formula: see text] is a positive singular solution for the following equation with a supercritical exponent [Formula: see text] where [Formula: see text] denotes the fractional Laplacian.

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