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Positive solution for a quasilinear equation with critical growth in $ℝ^N$

100%

Chen L., Chen C., Xiu Z.

Annales Polonici Mathematici

2016

tom 116

nr 3

251-262

We study the existence of positive solutions of the quasilinear problem ⎧ $-Δ_N u + V(x)|u|^{N-2}u = f(u,|∇u|^{N-2}∇u)$, $x ∈ ℝ^N$, ⎨ ⎩ u(x) > 0, $x∈ ℝ^N$, where $Δ_N u = div(|∇u|^{N-2}∇u)$ is the N-Laplacian operator, $V:ℝ^N → ℝ$ is a continuous potential, $f:ℝ × ℝ^N → ℝ$ is a continuous function. The main result follows from an iterative method based on Mountain Pass techniques.

2-local Lie isomorphisms of operator algebras on Banach spaces

100%

Chen L., Huang L., Lu F.

Studia Mathematica

2015

tom 229

nr 1

1-11

Let X and Y be complex Banach spaces of dimension greater than 2. We show that every 2-local Lie isomorphism ϕ of B(X) onto B(Y) has the form ϕ = φ + τ, where φ is an isomorphism or the negative of an anti-isomorphism of B(X) onto B(Y), and τ is a homogeneous map from B(X) into ℂI vanishing on all finite sums of commutators.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Studia Mathematica

2 Chen L.

1 Chen C.

1 Huang L.

1 Lu F.

1 Xiu Z.

1 2016

1 2015

Wyniki wyszukiwania

Positive solution for a quasilinear equation with critical growth in $ℝ^N$

2-local Lie isomorphisms of operator algebras on Banach spaces