Naasira, BentoumRapporteur: Rabah, Mecheter2025-07-072025-07-072025-06-15https://repository.univ-msila.dz/handle/123456789/46712In this work, we study the existence of weak solutions for a class of linear elliptic equations with lower-order terms and integrable data. More precisely, we consider problems of the form:   − u = 0 div( , M(x)∇u) + a(x)u = f(x), in on Ω ∂ , Ω,  where Ω ⊂ R N is a bounded domain, M(x) is an elliptic matrix, a(x) ∈ L 1 (Ω), and f ∈ L 1 (Ω). Since the right-hand side lies in L 1 (Ω), standard variational methods are not applicable. To address this, we construct a sequence of approximate problems whose solutions are well-defined, and establish uniform a priori estimates. Then, using compactness arguments and the theory of pseudo-monotone operators, we prove the existence of a weak solution to the original problem.enElliptic equationsweak solutionintegrable datapseudo-monotone operatorslower-order termsThesis