Semilinear elliptic equations on unbounded domains

1985 ◽  
Vol 190 (4) ◽  
pp. 519-525 ◽  
Author(s):  
G. R. Burton
Keyword(s):  
Elliptic Equations ◽  
Unbounded Domains ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic

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.

Existence and non-existence results for semilinear elliptic problems in unbounded domains

1982 ◽  
Vol 93 (1-2) ◽  
pp. 1-14 ◽  
Author(s):  
M. J. Esteban ◽  
P. L. Lions
Keyword(s):  
Elliptic Equations ◽  
Elliptic Problems ◽  
Unbounded Domains ◽  
Existence Results ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Image Position

SynopsisIn this paper, we prove various existence and non-existence results for semilinear elliptic problems in unbounded domains. In particular we prove for general classes of unbounded domains that there exists no solution distinct from 0 offor any smooth f satisfying f(0) = 0. This result is obtained by the use of new identities that solutions of semilinear elliptic equations satisfy.

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