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Nontrivial Solutions for Some Semilinear Elliptic Equations with Critical Sobolev Exponents
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@Article{JPDE-4-77,
author = {Wang Chuanfang, Xue Ruying},
title = {Nontrivial Solutions for Some Semilinear Elliptic Equations with Critical Sobolev Exponents},
journal = {Journal of Partial Differential Equations},
year = {1991},
volume = {4},
number = {1},
pages = {77--96},
abstract = { Let Ω be a bounded domain in R^4(n ≥ 4) with smooth boundary ∂Ω. We discuss the existence of nontrivial solutions of the Dirichlet problem {- Δu = a(x) |u|^{4/(a-2)}u + λu + g(x, u), \quad x ∈ Ω u = 0, \quad x ∈ ∂Ω where a(x) is a smooth function which is nonnegative on \overline{Ω} and positive somewhere, λ> 0 and λ ∉ σ(-Δ). We weaken the conditions on a(x) that are generally assumed in other papers dealing with this problem.},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5763.html}
}
TY - JOUR
T1 - Nontrivial Solutions for Some Semilinear Elliptic Equations with Critical Sobolev Exponents
AU - Wang Chuanfang, Xue Ruying
JO - Journal of Partial Differential Equations
VL - 1
SP - 77
EP - 96
PY - 1991
DA - 1991/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5763.html
KW - Semilinear elliptic equation
KW - Sobolev exponent
KW - Critical value
KW - Critical point
KW - (P • S) condition
AB - Let Ω be a bounded domain in R^4(n ≥ 4) with smooth boundary ∂Ω. We discuss the existence of nontrivial solutions of the Dirichlet problem {- Δu = a(x) |u|^{4/(a-2)}u + λu + g(x, u), \quad x ∈ Ω u = 0, \quad x ∈ ∂Ω where a(x) is a smooth function which is nonnegative on \overline{Ω} and positive somewhere, λ> 0 and λ ∉ σ(-Δ). We weaken the conditions on a(x) that are generally assumed in other papers dealing with this problem.
Wang Chuanfang, Xue Ruying. (1970). Nontrivial Solutions for Some Semilinear Elliptic Equations with Critical Sobolev Exponents.
Journal of Partial Differential Equations. 4 (1).
77-96.
doi:
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