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

• Autorzy: El Houssine Azroul , Abdelkrim Barbara , Meryem El Lekhlifi , Mohamed Rhoudaf
• Języki publikacji: EN

Abstrakty

EN

We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem
$-div(a(x,u,∇u)) + g(x,u) = f - divF$ in Ω,
where Ω is a bounded open domain of $ℝ^{N}$, N ≥ 2 and $a: Ω × ℝ× ℝ^{N} → ℝ^{N}$ 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 $∏_{i=1}^{N}L^{p'(·)}(Ω)$.

Kategorie tematyczne

• 35J66: Nonlinear boundary value problems for nonlinear elliptic equations
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 35J60: Nonlinear elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2012
• Tom: 39
• Numer: 3
• Strony: 339-364

Daty

wydano

2012

Twórcy

autor

El Houssine Azroul

• Laboratory LAMA, Department of Mathematics, Faculty of Sciences, Dhar-Mahraz, B.P. 1796, Atlas Fez, Morocco

autor

Abdelkrim Barbara

• Laboratory LAMA, Department of Mathematics, Faculty of Sciences, Dhar-Mahraz, B.P. 1796, Atlas Fez, Morocco

autor

Meryem El Lekhlifi

• Laboratory LAMA, Department of Mathematics, Faculty of Sciences, Dhar-Mahraz, B.P: 1796, Atlas Fez, Morocco

autor

Mohamed Rhoudaf

• Faculty of Science and Technology, Ziaten, km 10, old airport road, B.P. 416 Tangier, Morocco

Identyfikatory

DOI

10.4064/am39-3-8