In this paper we consider the quasilinear elliptic system ∆pu = uv, ∆pv = uv in a smooth bounded domain Ω ⊂ R , with the boundary conditions u = v = +∞ on ∂Ω. The operator ∆p stands for the… (More)

In this work we discuss existence, uniqueness and asymptotic profiles of positive solutions to the quasilinear problem { −Δpu+ a(x)up−1 = −u in Ω, |∇u|p−2 ∂u ∂ν = λup−1 on ∂Ω for λ ∈ R, where r > p −… (More)

In this paper we consider the elliptic system ∆u = u− v, ∆v = −u + v in Ω, where the exponents verify p, s > 1, q, r > 0 and ps > qr and Ω is a smooth bounded domain of R . First, we show existence… (More)

In this work we consider the nonlocal stationary nonlinear problem (J ∗ u)(x) − u(x) = −λu(x) + a(x)u(x) in a domain Ω, with the Dirichlet boundary condition u = 0 in R \ Ω and p > 1. The kernel J… (More)

We study the problem { −∆pu = |u|q−2u, x ∈ Ω, |∇u|p−2 ∂u ∂ν = λ|u|p−2u, x ∈ ∂Ω, where Ω ⊂ R is a bounded smooth domain, ν is the outward unit normal at ∂Ω and λ > 0 is regarded as a bifurcation… (More)

In this paper we analyze some properties of the principal eigenvalue λ1(Ω) of the nonlocal Dirichlet problem (J∗u)(x)−u(x) = −λu(x) in Ω with u(x) = 0 in R \Ω. Here Ω is a smooth bounded domain of R… (More)