ASYMPTOTIC BEHAVIOUR OF SOLUTIONS TO SEMILINEAR ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS

EQUADIFF 2003 ◽  
2005 ◽  
Author(s):  
G. V. GRISHINA
Keyword(s):  
Asymptotic Behaviour ◽  
Elliptic Equations ◽  
Unbounded Domains ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Asymptotic Behaviour Of Solutions

Axial symmetry of solutions to semilinear elliptic equations in unbounded domains

2003 ◽  
Vol 133 (5) ◽  
pp. 1175-1192 ◽  
Author(s):  
Eugenio Montefusco
Keyword(s):  
Axial Symmetry ◽  
Elliptic Equations ◽  
Morse Index ◽  
Unbounded Domains ◽  
Semilinear Elliptic Equations ◽  
Bounded Domains ◽  
Strictly Convex ◽  
Semilinear Elliptic

In this paper we study the problem of the axial symmetry of solutions of some semilinear elliptic equations in unbounded domains. Assuming that the solutions have Morse index one and that the nonlinearity is strictly convex in the second variable, we are able to prove several symmetry results in Rn and in the exterior of a ball. The case of some bounded domains is also discussed.

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