The aim of this work is to study the existence of solutions of a nonlinear value boundary problem with L 1 data with truncation and epiconvergence method.

The aim of this work is to study the limit behavior of weak solutions of athermal problem (where the heat loss is considered), of a containing structure, an oscillatingthin layer of thickness, periodicity and heat loss parameter depending of $\varepsilon$. Theepiconvergence method is considered to find the limit problems with interface conditions.

This work is devoted to study the limit behavior of weak solutions of an elliptic problem with variable exponent, in a containing structure, of an oscillating nanolayer of thickness and periodicity parameter depending on ε . The generalized Sobolev space is constructed, and the epiconvergence method is considered to find the limit problem with interface conditions.

The aim of this paper, is to study the limit behavior of the solution of a convex elasticity problem with a negative power type, of a containing structure, an elastic thin oscillating layer of thickness and periodicity parameter depending of a small enough parameter ε. The epi-convergence method is considered to find the limit problems with interface conditions.

Abstract. We study the asymptotic behavior of a thermal problem, of a containing structure, an oscillating thin layer of thickness and conductivity depending of ε. We use the the epi-convergence method to find the limit problems with interface conditions. The obtained results are tested numerically.