Abita, Rahmoune2020-02-162020-02-162019http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/19256In this study, we prove the existence of local solution for a quasi linear generalized parabolic equation with nonlocal boundary conditions for an elliptic operator involving the variable-exponent nonlinearities, using Faedo-Galerkin arguments and compactness method.Nonlocal boundary conditions, quasi-linear parabolic equations, generalized Lebesgue space and Sobolev spaces with variable exponenArticle