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We show the existence of positive solutions for a class of singular elliptic systems with convection term. The approach combines sub and supersolution method with the pseudomonotone operator theory and perturbation arguments involving singular terms.

In this work we study the existence of nontrivial solution for the following class of multivalued quasilinear problems −div(ϕ(|∇u|)∇u) − b(u)u ∈ λ∂F (x, u) in Ω, u = 0 on ∂Ω where Ω ⊂ R N is a bounded domain, N ≥ 2 and ∂F (x, u) is a generalized gradient of F (x, t) with respect to t. The main tools utilized are Variational Methods for Locally Lipschitz… (More)

In this note we use variational arguments {namely Ekeland's Principle and the Mountain Pass Theorem{ to study the equation ?u + a(x)u = u q + u 2 ?1 in R N : The main concern is overcoming compactness diiculties due both to the unboundedness of the domain R N , and the presence of the critical exponent 2 = 2N=(N ? 2).

- FRANCISCO JÚLIO, S. A. CORRÊA, Claudianor O. Alves
- 2006

We investigate the questions of existence of positive solution for the nonlocal problem −M(u 2)Δu = f (λ,u) in Ω and u = 0 on ∂Ω, where Ω is a bounded smooth domain of R N , and M and f are continuous functions. distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided… (More)

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