Elliptic singular problems with a quadratic gradient term
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Data
2009
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Resumo
We deal with existence and nonexistence of positive classical solutions
to the Dirichlet problem for the quasilinear singular elliptic equation
−∆u = λ β(u) |∇u| 2 + Ψ(x) in Ω, where Ω ⊂ R N (N ≥ 3) is a domain
with smooth boundary ∂Ω, λ > 0 is a real parameter, β : (0, ∞) → (0, ∞)
s→0
is a C 1 -function, possibly singular at zero in the sense that β(s) → ∞,
and Ψ : Ω → [0, ∞) is continuous. No monotonicity condition whatsoever
is imposed upon β.
Descrição
Palavras-chave
Elliptic equations, Singular problems, Gradient term, Lower and upper solutions, Fixed points
Citação
GONÇALVES, J. V.; MELO, A. L.; SANTOS, C. A. Elliptic singular problems with a quadratic gradient term. Matemática Contemporânea, Rio de Janeiro, v. 36, p. 107-129, 2009.