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Nontrivial Solutions for Some Semilinear Elliptic Equations with Critical Sobolev Exponents
Authors:Wang Chuanfang  Xue Ruying
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.
Keywords:Semilinear elliptic equation                                                                                                  Sobolev exponent                                                                                                  Critical value                                                                                                Critical point                                                                                                  (P • S) condition
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