Symmetry breaking for semilinear elliptic equations on sectorial domains in ℝ2
1991 ◽
Vol 118
(3-4)
◽
pp. 327-353
Keyword(s):
SynopsisWe first study the Poisson equation Δu =fin Ώω,and, where Ωω= {(rcos θ,rsin θ): 0<r<1, θ ∈(0,ω)} is a sector in ℝ2, ω ∈ (0, 2π), Г0= {(cos θ, sin θ): θ ∈ (0, ω)} and Г1= ∂Ωω− Г0,band λ are in ℝ1. We obtain Schauder-type estimates and Fredholm alternative theory for the problem. We then study the symmetry breaking problem for the Gel'fand equation Δu+ λeu= 0 in Ωωand obtain a complete picture about the relationships among three parameters λ,b, and ω in the problem.
1990 ◽
Vol 89
(2)
◽
pp. 364-409
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1994 ◽
Vol 126
(4)
◽
pp. 299-331
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1989 ◽
Vol 26
(1-2)
◽
pp. 79-96
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Keyword(s):
1995 ◽
Vol 54
(2)
◽
pp. 125-137
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1986 ◽
Vol 95
(3)
◽
pp. 217-225
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2010 ◽
Vol 40
(3-4)
◽
pp. 295-317
◽
Keyword(s):
1986 ◽
Vol 105
(3)
◽
pp. 415-441
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