Research Communication | Open Access
Volume 2021 | Communication ID 139
Volume 2021 | Communication ID 139
| Existence of solutions for an elliptic equation in Sobolev space with variable exponent |
Aharrouch Benali, Bennouna Jaouad
Received |
Accepted |
Published |
January 29, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: Nonlinear elliptical equations have been studied in the framework of Lebesgue and Sobolev spaces for years by several authors, I cite for example the following documents [1, 2]. In the recent years, elliptic equations with non-linearities involving non-constant exponents have attracted increasing attention, see for example the results in the document [3, 4, 5]. In this article, we study the Direchlet problem -div a (x, u, Du) = f-div g, a : Ω× R× RN ------>R a Carathéodory function, f in Lm(.)( Ω) and g in (Lp’(.)( Ω))N. with Ω is an open bounded domain in ...