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T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum

El Houssine Azroul; Abdelkrim Barbara; Meryem El Lekhlifi; Mohamed Rhoudaf — 2012

Applicationes Mathematicae

We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem $- d i v (a (x, u, \nabla u)) + g (x, u) = f - d i v F$ in Ω, where Ω is a bounded open domain of $ℝ^{N}$ , N ≥ 2 and $a : Ω \times ℝ \times ℝ^{N} \to ℝ^{N}$ is a Carathéodory function satisfying the natural growth condition and the coercivity condition, but with only a weak monotonicity condition. The right hand side f lies in L¹(Ω) and F belongs to $\prod_{i = 1}^{N} L^{p^{'} (\cdot)} (Ω)$ .

Entropy solutions for nonhomogeneous anisotropic $Δ_{p ⃗ (\cdot)}$ problems

Elhoussine Azroul; Abdelkrim Barbara; Mohamed Badr Benboubker; Hassane Hjiaj — 2014

Applicationes Mathematicae

We study a class of anisotropic nonlinear elliptic equations with variable exponent p⃗(·) growth. We obtain the existence of entropy solutions by using the truncation technique and some a priori estimates.

Quasilinear elliptic problems with nonstandard growth.

Benboubker, Mohamed Badr; Azroul, Elhoussine; Barbara, Abdelkrim — 2011

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Currently displaying 1 – 3 of 3

T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum

Entropy solutions for nonhomogeneous anisotropic $Δ_{p ⃗ (\cdot)}$ problems

Quasilinear elliptic problems with nonstandard growth.

Advanced Search

Formula preview

Currently displaying 1 – 3 of 3

T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum

Entropy solutions for nonhomogeneous anisotropic Δ p ⃗ ( · ) problems

Quasilinear elliptic problems with nonstandard growth.

Entropy solutions for nonhomogeneous anisotropic $Δ_{p ⃗ (\cdot)}$ problems