Some existence results for superlinear elliptic boundary value problems involving critical exponents
The existence of solutions to the problem −Δu − λu = u¦u¦ 2∗ − 2 in Ω u¦ ∂Ω = 0 is studied. For an arbitrary domain Ω ⊂ R n , if λ ϵ ]0, λ 1[ and n ⩾ 6, the existence of solutions of changing sign is obtained. If Ω = B R (0) ⊂ R n , λ ϵ ]0, λ 1[, and n ⩾ 7, infinitely many radial solutions to this p...
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Published in | Journal of functional analysis Vol. 69; no. 3; pp. 289 - 306 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Orlando, FL
Elsevier Inc
01.12.1986
San Diego, CA Academic Press Brugge |
Subjects | |
Online Access | Get full text |
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Summary: | The existence of solutions to the problem
−Δu − λu = u¦u¦
2∗ − 2
in Ω
u¦
∂Ω = 0
is studied. For an arbitrary domain Ω ⊂
R
n
, if λ ϵ ]0,
λ
1[ and
n ⩾ 6, the existence of solutions of changing sign is obtained. If Ω =
B
R
(0) ⊂
R
n
, λ ϵ ]0,
λ
1[, and
n ⩾ 7, infinitely many radial solutions to this problem are exhibited, characterized by the number of nodes they possess. |
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ISSN: | 0022-1236 1096-0783 |
DOI: | 10.1016/0022-1236(86)90094-7 |