Abstract
The existence of positive solutions is discussed for some nonlinear elliptic equations involving the nonlinear terms with the growth order of super-critical exponents in exterior domains of balls such as -Δu = u β in Ω, ((N + 2)/(N - 2) < β), u = 0 on ∂B, with Ω = ℝN\Ω̄ where Ω0 is the open ball. To recover the compactness of the embedding L β+1(Ω) ⊂ H0 1(Ω, we work in the class of radially symmetric functions and introduce a new transformation, which reduces our problems to some nonlinear elliptic equations in annuli but with coefficients which have some singularity on the boundary. The difficulty caused by the singularity on the boundary will be managed by the arguments developed in our previous work.
| Original language | English |
|---|---|
| Pages (from-to) | 323-333 |
| Number of pages | 11 |
| Journal | Discrete and Continuous Dynamical Systems |
| Volume | 19 |
| Issue number | 2 |
| Publication status | Published - 2007 Oct |
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Keywords
- Exterior domain
- P-Laplacian
- Supercritical exponent
ASJC Scopus subject areas
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Analysis
Cite this
Existence of nontrivial solutions for some elliptic equations with supercritical nonlinearity in exterior domains. / Hashimoto, Satoshi; Otani, Mitsuharu.
In: Discrete and Continuous Dynamical Systems, Vol. 19, No. 2, 10.2007, p. 323-333.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Existence of nontrivial solutions for some elliptic equations with supercritical nonlinearity in exterior domains
AU - Hashimoto, Satoshi
AU - Otani, Mitsuharu
PY - 2007/10
Y1 - 2007/10
N2 - The existence of positive solutions is discussed for some nonlinear elliptic equations involving the nonlinear terms with the growth order of super-critical exponents in exterior domains of balls such as -Δu = u β in Ω, ((N + 2)/(N - 2) < β), u = 0 on ∂B, with Ω = ℝN\Ω̄ where Ω0 is the open ball. To recover the compactness of the embedding L β+1(Ω) ⊂ H0 1(Ω, we work in the class of radially symmetric functions and introduce a new transformation, which reduces our problems to some nonlinear elliptic equations in annuli but with coefficients which have some singularity on the boundary. The difficulty caused by the singularity on the boundary will be managed by the arguments developed in our previous work.
AB - The existence of positive solutions is discussed for some nonlinear elliptic equations involving the nonlinear terms with the growth order of super-critical exponents in exterior domains of balls such as -Δu = u β in Ω, ((N + 2)/(N - 2) < β), u = 0 on ∂B, with Ω = ℝN\Ω̄ where Ω0 is the open ball. To recover the compactness of the embedding L β+1(Ω) ⊂ H0 1(Ω, we work in the class of radially symmetric functions and introduce a new transformation, which reduces our problems to some nonlinear elliptic equations in annuli but with coefficients which have some singularity on the boundary. The difficulty caused by the singularity on the boundary will be managed by the arguments developed in our previous work.
KW - Exterior domain
KW - P-Laplacian
KW - Supercritical exponent
UR - http://www.scopus.com/inward/record.url?scp=36248976091&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=36248976091&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:36248976091
VL - 19
SP - 323
EP - 333
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
SN - 1078-0947
IS - 2
ER -