Author(s)

El Houcine Rami, Abdelkrim Barbara, El Houssine Azroul

Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco.

Using the theory of weighted Sobolev spaces with variable exponent and the L¹-version on Minty’s lemma, we investigate the existence of solutions for some nonhomogeneous Dirichlet problems generated by the Leray-Lions operator of divergence form, with right-hand side measure. Among the interest of this article is the given of a very important approach to ensure the existence of a weak solution of this type of problem and of generalization to a system with the minimum of conditions.

Nonhomogeneous Elliptic Equations, Dirichlet Problems, Weighted Sobolev Spaces with Variable Exponent, Minty’s Lemma, T-ν-p(x)-Solutions

Rami, E. , Barbara, A. and Azroul, E. (2021) Existence of T-ν-p(x)-Solution of a Nonhomogeneous Elliptic Problem with Right Hand Side Measure. Journal of Applied Mathematics and Physics, 9, 2717-2732. doi: 10.4236/jamp.2021.911175.