Several authors studied the system of elasticity with laws of particular behavior and using various techniques in constant exponents Sobolev spaces. In this article we consider a Dirichlet problem for nonlinear elasticity system with laws of general behavior. The coefficients of elasticity depends on and the density of the volumetric forces depends on the displacement. We consider this problem as a Leray-Lions operator and the main aim of this paper is to apply Galerkin techniques and monotone operator theory to prove a theorem of existence and uniqueness.

Key Words: Existence and uniqueness, spaces of Lebesgue and Sobolev with variable exponents, Dirichlet problem, nonlinear elasticity system, operator of Leray-Lions.

2010 Mathematics Subject Classification: Primary 35J45; Secondary 35J55, 35A05, 35A07, 35A15.

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